Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991
8th Edition
ISBN: 9781259731709
Author: ROSEN
Publisher: MCG
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 10, Problem 17WP
To determine
Some of the strategies and algorithms used to solve the travelling salesperson problem.
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
A family has two cars. The first car has a fuel efficiency of 16 kilometers per liter of gas and the second has a fuel efficiency of 18 kilometers per liter of gas.
During one particular week, the two cars went a combined total of 3150 kilometers, for a total gas consumption of 190 liters. How many liters were consumed
by each of the two cars that week?
Note that the ALEKS graphing calculator can be used to make computations easier.
First car:
liters
?
Second car:|liters
Imagine you are in a city that has a grid of streets with perfectly square blocks and that the only way to get from one intersection to another is to follow the block system.
How many blocks will you have to walk (or pay the cabdriver for) if you want to get from the intersection of 10th Ave and 25th Street to the intersection of 6th Ave and 28th Street? If you had a jet pack and could fly over the buildings, how many blocks in length would the shortest path be? How does this compare to #1? (Hint: Pythagorean Theorem)
There are many real-life problems like the traveling salesperson problem.For example, the telephone company must decide on the most efficient route for a worker to collect the money from public telephones. Giveanother example.
Chapter 10 Solutions
Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991
Ch. 10.1 - Draw graph models, stating the type of graph...Ch. 10.1 - Prob. 2ECh. 10.1 - For Exercises 3-5, determine whether the graph...Ch. 10.1 - For Exercises 3-5, determine whether the graph...Ch. 10.1 - For Exercises 3-5, determine whether the graph...Ch. 10.1 - For Exercises 3-5, determine whether the graph...Ch. 10.1 - For Exercises 3-5, determine whether the graph...Ch. 10.1 - For Exercises 3-5, determine whether the graph...Ch. 10.1 - For Exercises 3-5, determine whether the graph...Ch. 10.1 - For each undirected graph in Exercises 3-9 that is...
Ch. 10.1 - Let G be a simple graph. Show that the relation R...Ch. 10.1 - Let G be an undirected graph with a loop at every...Ch. 10.1 - The intersection graphof a collection of...Ch. 10.1 - Use the niche overlap graph inFigure 11to...Ch. 10.1 - Construct a niche overlap graph for six species of...Ch. 10.1 - Draw the acquaintanceship graph that represents...Ch. 10.1 - Prob. 17ECh. 10.1 - Who can influence Fred and whom can Fred influence...Ch. 10.1 - Construct an influence graph for the board members...Ch. 10.1 - The word apple can refer to a plant, a food, or a...Ch. 10.1 - Prob. 21ECh. 10.1 - Which other teams did Team 4 beat and which teams...Ch. 10.1 - In a round-robin tournament the Tigers beat the...Ch. 10.1 - Construct the call graph for a set of seven...Ch. 10.1 - Explain how the two telephone call graphs for...Ch. 10.1 - a) Explain how graphs can be used to model...Ch. 10.1 - How can a graph that models e-mail messages sent...Ch. 10.1 - How can a graph that models e-mail messages sent...Ch. 10.1 - Describe a graph model that represents whether...Ch. 10.1 - Describe a graph model that represents a subway...Ch. 10.1 - Prob. 31ECh. 10.1 - Describe a graph model that represents the...Ch. 10.1 - Describe a graph model that represents traditional...Ch. 10.1 - Prob. 34ECh. 10.1 - Construct a precedence graph for the following...Ch. 10.1 - Describe a discrete structure based on a graph...Ch. 10.1 - Describe a discrete structure based on a graph...Ch. 10.1 - Prob. 38ECh. 10.2 - In Exercises 1-3 find the number of vertices, the...Ch. 10.2 - In Exercises 1-3 find the number of vertices, the...Ch. 10.2 - Prob. 3ECh. 10.2 - Prob. 4ECh. 10.2 - Can a simple graph exist with 15 vertices each of...Ch. 10.2 - Show that the sum, over the set of people at a...Ch. 10.2 - Prob. 7ECh. 10.2 - Prob. 8ECh. 10.2 - Prob. 9ECh. 10.2 - For each of the graphs in Exercises 7-9 determine...Ch. 10.2 - Construct the underlying undirected graph for the...Ch. 10.2 - What does the degree of a vertex represent in the...Ch. 10.2 - Prob. 13ECh. 10.2 - What does the degree of a vertex in the Hollywood...Ch. 10.2 - What do the in-degree and the out-degree of a...Ch. 10.2 - Prob. 16ECh. 10.2 - Prob. 17ECh. 10.2 - Show that in a simple graph with at least two...Ch. 10.2 - Use Exercise 18 to show that in a group of people,...Ch. 10.2 - Prob. 20ECh. 10.2 - In Exercises 21-25 determine whether the graph is...Ch. 10.2 - In Exercises 21-25 determine whether the graph is...Ch. 10.2 - Prob. 23ECh. 10.2 - Prob. 24ECh. 10.2 - In Exercises 21-25 determine whether the graph is...Ch. 10.2 - For which values ofnare these graphs bipartite?...Ch. 10.2 - Suppose that therearefour employees in the...Ch. 10.2 - Suppose that a new company has five employees:...Ch. 10.2 - Suppose that therearefive young women and five...Ch. 10.2 - Suppose that therearefive young women and six...Ch. 10.2 - Prob. 31ECh. 10.2 - Each of Exercises 31-33 can be solved using Hall's...Ch. 10.2 - Prob. 33ECh. 10.2 - Prob. 34ECh. 10.2 - Each of Exercises 31-33 can be solved using Hall's...Ch. 10.2 - Prob. 36ECh. 10.2 - How many vertices and how many edges do these...Ch. 10.2 - Prob. 38ECh. 10.2 - Prob. 39ECh. 10.2 - Prob. 40ECh. 10.2 - Prob. 41ECh. 10.2 - How many edges does a graph have if its degree...Ch. 10.2 - Prob. 43ECh. 10.2 - Determine whether each of these sequences is...Ch. 10.2 - Prob. 45ECh. 10.2 - Prob. 46ECh. 10.2 - Prob. 47ECh. 10.2 - Prob. 48ECh. 10.2 - Prob. 49ECh. 10.2 - Prob. 50ECh. 10.2 - Prob. 51ECh. 10.2 - Prob. 52ECh. 10.2 - Draw all sub graphs of this graph.Ch. 10.2 - Let G be a graph with vertices and e edges. Let M...Ch. 10.2 - For which values ofnare these graphs regular? a)...Ch. 10.2 - Prob. 56ECh. 10.2 - Prob. 57ECh. 10.2 - In Exercises 58-60 find the union of the given...Ch. 10.2 - Prob. 59ECh. 10.2 - In Exercises 58-60 find the union of the given...Ch. 10.2 - The complementarygraphGof a simple graph G has the...Ch. 10.2 - IfGis a simple graph with 15 edges andGhas 13...Ch. 10.2 - Prob. 63ECh. 10.2 - Prob. 64ECh. 10.2 - Prob. 65ECh. 10.2 - Prob. 66ECh. 10.2 - Prob. 67ECh. 10.2 - Describe an algorithm to decide whether a graph is...Ch. 10.2 - Theconverseof a directed graph G = (V, E), denoted...Ch. 10.2 - Theconverseof a directed graph G = (V, E), denoted...Ch. 10.2 - Prob. 71ECh. 10.2 - Prob. 72ECh. 10.2 - Theconverseof a directed graph G = (V, E), denoted...Ch. 10.2 - Prob. 74ECh. 10.2 - Theconverseof a directed graph G = (V, E), denoted...Ch. 10.3 - In Exercises 1-4 use an adjacency list to...Ch. 10.3 - Prob. 2ECh. 10.3 - Prob. 3ECh. 10.3 - Prob. 4ECh. 10.3 - Represent the graph in Exercise 1 with an...Ch. 10.3 - Represent the graph in Exercise 2 with an...Ch. 10.3 - Represent the graph in Exercise 3 with an...Ch. 10.3 - Represent the graph in Exercise 4 with an...Ch. 10.3 - Represent each of these graphs with an adjacency...Ch. 10.3 - In Exercises 10-12 draw a graph with the given...Ch. 10.3 - In Exercises 10-12 draw a graph with the given...Ch. 10.3 - In Exercises 10-12 draw a graph with the given...Ch. 10.3 - In Exercises 13-15 represent the given graph using...Ch. 10.3 - In Exercises 13-15 represent the given graph using...Ch. 10.3 - In Exercises 13-15 represent the given graph using...Ch. 10.3 - In Exercises 16-18 draw an undirected graph...Ch. 10.3 - In Exercises 16-18 draw an undirected graph...Ch. 10.3 - In Exercises 16-18 draw an undirected graph...Ch. 10.3 - Prob. 19ECh. 10.3 - In Exercises 19-21 find the adjacency matrix of...Ch. 10.3 - In Exercises 19-21 find the adjacency matrix of...Ch. 10.3 - In Exercises 22-24 draw the graph represented by...Ch. 10.3 - In Exercises 22-24 draw the graph represented by...Ch. 10.3 - In Exercises22-24 draw the graph represented by...Ch. 10.3 - Find the density of the graph in a)Figure...Ch. 10.3 - Prob. 26ECh. 10.3 - Prob. 27ECh. 10.3 - Prob. 28ECh. 10.3 - Is every zero-one square matrix that is symmetric...Ch. 10.3 - Prob. 30ECh. 10.3 - Prob. 31ECh. 10.3 - Prob. 32ECh. 10.3 - What is me sum of me entries in a column of me...Ch. 10.3 - What is the sum of the entries in a row of the...Ch. 10.3 - What is the sum of the entries in a column of the...Ch. 10.3 - Find an adjacency matrix for each of these graphs....Ch. 10.3 - Prob. 37ECh. 10.3 - In Exercises 38-48 determine whether the given...Ch. 10.3 - In Exercises 38-48 determine whether the given...Ch. 10.3 - In Exercises 38-48 determine whether the given...Ch. 10.3 - In Exercises 38-48 determine whether the given...Ch. 10.3 - In Exercises 38-48 determine whether the given...Ch. 10.3 - In Exercises 38-48 determine whether the given...Ch. 10.3 - In Exercises 38-48 determine whether the given...Ch. 10.3 - In Exercises 38-48 determine whether the given...Ch. 10.3 - In Exercises 38-48 determine whether the given...Ch. 10.3 - In Exercises 38-48 determine whether the given...Ch. 10.3 - In Exercises 38-48 determine whether the given...Ch. 10.3 - Show that isomorphism of simple graphs is an...Ch. 10.3 - Prob. 50ECh. 10.3 - Prob. 51ECh. 10.3 - Prob. 52ECh. 10.3 - Prob. 53ECh. 10.3 - Prob. 54ECh. 10.3 - Prob. 55ECh. 10.3 - Prob. 56ECh. 10.3 - Prob. 57ECh. 10.3 - How many non isomorphic simple graphs are there...Ch. 10.3 - How many nonisomorphic simple graphs are there...Ch. 10.3 - How many nonisomorphic simple graphs are there...Ch. 10.3 - Prob. 61ECh. 10.3 - Prob. 62ECh. 10.3 - Are the simple graphswiththe following adjacency...Ch. 10.3 - Determine whether the graphs without loops with...Ch. 10.3 - Prob. 65ECh. 10.3 - Prob. 66ECh. 10.3 - Prob. 67ECh. 10.3 - In Exercises 67-70 determine whether the given...Ch. 10.3 - Prob. 69ECh. 10.3 - In Exercises 67-70 determine whether the given...Ch. 10.3 - Show that ifGand H are isomorphic directed graphs,...Ch. 10.3 - Show that the property that a graph is bipartite...Ch. 10.3 - Prob. 73ECh. 10.3 - Prob. 74ECh. 10.3 - Prob. 75ECh. 10.3 - How much storage is needed to represent a simple...Ch. 10.3 - A devil's pairfor a purported isomorphism testis a...Ch. 10.3 - Prob. 78ECh. 10.4 - Does each of these lists of vertices form a path...Ch. 10.4 - Does each of these lists of vertices form a path...Ch. 10.4 - In Exercises 3-5 determine whether the given graph...Ch. 10.4 - In Exercises 3-5 determine whether the given graph...Ch. 10.4 - In Exercises 3-5 determine whether the given graph...Ch. 10.4 - How many connected components does each of the...Ch. 10.4 - What do the connected components of...Ch. 10.4 - Prob. 8ECh. 10.4 - Explain why in the collaboration graph of...Ch. 10.4 - In the Hollywood graph (see Example 3 inSection...Ch. 10.4 - Determine whether each of these graphs is strongly...Ch. 10.4 - Determine whether each of these graphs is strongly...Ch. 10.4 - What do the strongly connected components of a...Ch. 10.4 - Find the strongly connected components of each of...Ch. 10.4 - Find the strongly connected components of each of...Ch. 10.4 - Suppose that G=(V, E) is a directed graph. A...Ch. 10.4 - Prob. 17ECh. 10.4 - Prob. 18ECh. 10.4 - Find the number of paths of length n between two...Ch. 10.4 - Use paths either to show that these graphs are not...Ch. 10.4 - Prob. 21ECh. 10.4 - Prob. 22ECh. 10.4 - Prob. 23ECh. 10.4 - Find the number of paths of length n between any...Ch. 10.4 - Find the number of paths of length n between any...Ch. 10.4 - Find the number of paths between c andd inthe...Ch. 10.4 - Prob. 27ECh. 10.4 - Prob. 28ECh. 10.4 - Prob. 29ECh. 10.4 - Show that in every simple graph there is a path...Ch. 10.4 - In Exercises 31-33 find all the cut vertices of...Ch. 10.4 - In Exercises 31-33 find all the cut vertices of...Ch. 10.4 - Prob. 33ECh. 10.4 - Find all the cut edges in the graph sin Exercises...Ch. 10.4 - Prob. 35ECh. 10.4 - Prob. 36ECh. 10.4 - Prob. 37ECh. 10.4 - Prob. 38ECh. 10.4 - Prob. 39ECh. 10.4 - A vertex basis in a directed graph G is aminimal...Ch. 10.4 - Prob. 41ECh. 10.4 - Prob. 42ECh. 10.4 - Prob. 43ECh. 10.4 - Use Exercise43 to show that a simple graph with n...Ch. 10.4 - Show that a simple graph G withnvertices is...Ch. 10.4 - Prob. 46ECh. 10.4 - How many nonisom orphic connected simple graphs...Ch. 10.4 - Show that each of the following graphs has no cut...Ch. 10.4 - Prob. 49ECh. 10.4 - For each of these graphs, find(G),(G),and...Ch. 10.4 - Show that if G is a connected graph, then it is...Ch. 10.4 - Show that if G is a connected graph withnvertices...Ch. 10.4 - Find(Km,n) and(Km,n), wherem andnare positive...Ch. 10.4 - Construct a graphG with(G) - 1,(G) -2, and...Ch. 10.4 - Show that if G is a graph, then(G) (G).Ch. 10.4 - ExplainhowTheorem 2canbe used to find the length...Ch. 10.4 - Prob. 57ECh. 10.4 - Prob. 58ECh. 10.4 - Prob. 59ECh. 10.4 - Show that the existence of a simple circuit of...Ch. 10.4 - Prob. 61ECh. 10.4 - Use Exercise 61 to show that the...Ch. 10.4 - Prob. 63ECh. 10.4 - In an old puzzle attributed to Alcuin of York...Ch. 10.4 - Use a graph model and a path in your graph, as in...Ch. 10.4 - Prob. 66ECh. 10.5 - In Exercises 1-8 determine whether the given graph...Ch. 10.5 - In Exercises 1-8 determine whether the given graph...Ch. 10.5 - Prob. 3ECh. 10.5 - In Exercises 1-8 determine whether the given graph...Ch. 10.5 - In Exercises 1-8 determine whether the given graph...Ch. 10.5 - In Exercises 1-8 determine whether the given graph...Ch. 10.5 - In Exercises 1-8 determine whether the given graph...Ch. 10.5 - In Exercises 1-8 determine whether the given graph...Ch. 10.5 - Suppose that in addition to the seven bridges of...Ch. 10.5 - Prob. 10ECh. 10.5 - When can the centerlines of the streets in a city...Ch. 10.5 - Devise a procedure, similar to Algorithm 1, for...Ch. 10.5 - In Exercises 13-15 determine whether the picture...Ch. 10.5 - In Exercises 13-15 determine whether the picture...Ch. 10.5 - In Exercises 13-15 determine whether the picture...Ch. 10.5 - Show that a directed multigraph having no isolated...Ch. 10.5 - Show that a directed multigraph having no isolated...Ch. 10.5 - In Exercises 18-23 determine whether the directed...Ch. 10.5 - In Exercises 18-23 determine whether the directed...Ch. 10.5 - In Exercises 18-23 determine whether the directed...Ch. 10.5 - In Exercises 18-23 determine whether the directed...Ch. 10.5 - In Exercises 18-23 determine whether the directed...Ch. 10.5 - In Exercises 18-23 determine whether the directed...Ch. 10.5 - Devise an algorithm for constructing Euler...Ch. 10.5 - Devise an algorithm for constructing Euler paths...Ch. 10.5 - For which values of n do thesegraphs have an...Ch. 10.5 - For whichvalues ofndo the graphs in Exercise 26...Ch. 10.5 - For which values ofmandn.does the complete...Ch. 10.5 - Find the least number of times it is necessary to...Ch. 10.5 - In Exercises 30-36 determine whether the given...Ch. 10.5 - In Exercises 30-36 determine whether the given...Ch. 10.5 - In Exercises 30-36 determine whether the given...Ch. 10.5 - In Exercises 30-36 determine whether the given...Ch. 10.5 - In Exercises 30-36 determine whether the given...Ch. 10.5 - Prob. 35ECh. 10.5 - In Exercises 30-36 determine whether the given...Ch. 10.5 - Does the graph in Exercise 30 have a Hamilton...Ch. 10.5 - Does the graph in Exercise 31 have a Hamilton...Ch. 10.5 - Does the graph in Exercise 32 have a Hamilton...Ch. 10.5 - Does the graph in Exercise 33 have a Hamilton...Ch. 10.5 - Does the graph in Exercise 34 have a Hamilton...Ch. 10.5 - Does the graph in Exercise 35 have a Hamilton...Ch. 10.5 - Does the graph inExercise 36 have a Hamilton path?...Ch. 10.5 - For which values ofn.do the graphs in Exercise 26...Ch. 10.5 - For which values of m andndoes the complete...Ch. 10.5 - Show that thePetersen graph,shown here, does not...Ch. 10.5 - For each of these graphs, determine (i) whether...Ch. 10.5 - Can you find a simple graph with n vertices...Ch. 10.5 - Show that there is a Gray code of order whenever n...Ch. 10.5 - Fleury’s algorithm, published in 1883, constricts...Ch. 10.5 - Express Fleury's algorithm in pseudocode.Ch. 10.5 - Prob. 52ECh. 10.5 - Give a variant of Fleury's algorithm to produce...Ch. 10.5 - A diagnostic message can be sent out over a...Ch. 10.5 - Show that a bipartite graph with an odd number of...Ch. 10.5 - A knightis a chess piece that can move either two...Ch. 10.5 - A knightis a chess piece that can move either two...Ch. 10.5 - a) Show that finding a knights tour on...Ch. 10.5 - Show that there is a knight's tour on...Ch. 10.5 - Show that there is no knight's tour on...Ch. 10.5 - Show that there is no knight's tour on...Ch. 10.5 - Show that the graph representing the 1egal moves...Ch. 10.5 - Show that there is no reentrant knight's tour on...Ch. 10.5 - Show that there is a knight's tour on...Ch. 10.5 - The parts of this exercise outline a proof of...Ch. 10.5 - Show that if u and v are nondjacent vertices in a...Ch. 10.5 - Show that this graph doesnothave a Hamilton...Ch. 10.5 - Prob. 68ECh. 10.6 - For each of these problems about a subway system,...Ch. 10.6 - In Exercises 2-4 find the length of a shortest...Ch. 10.6 - In Exercises 2-4 find the length of a shortest...Ch. 10.6 - In Exercises 2-4 find the length of a shortest...Ch. 10.6 - Find a shortest path betweenaandzin each of the...Ch. 10.6 - Prob. 6ECh. 10.6 - Find shortest paths in the weighted graph in...Ch. 10.6 - Find a shortest path (in mileage) between each of...Ch. 10.6 - Find a combination of flights with the least total...Ch. 10.6 - Find a least expensive combination of flights...Ch. 10.6 - Find a shortest route (in distance) between...Ch. 10.6 - Find a routs with the shortest response time...Ch. 10.6 - Find a least expensive route, in monthly lease...Ch. 10.6 - Explain how to find a path mm the least number of...Ch. 10.6 - Exend Dijkstea's algorithm for finding the length...Ch. 10.6 - Extend Dijkstra's algorithm for finding the length...Ch. 10.6 - The weighted graphs in the figures here show some...Ch. 10.6 - Is a shortest path between two vertices in a...Ch. 10.6 - What are some applications where it is necessary...Ch. 10.6 - What is the length of a longest simple path in the...Ch. 10.6 - Floyd 's algorithm,displayed as Algorithm 2, can...Ch. 10.6 - Prove that Floyd's algorithm determines the...Ch. 10.6 - Give a big-0 estimate of the number of operations...Ch. 10.6 - Show that Dijkstra's algorithm may not work if...Ch. 10.6 - Solve the traveling salesperson problem for this...Ch. 10.6 - Solve the traveling salesperson problem far this...Ch. 10.6 - Find a route with the least total airfare that...Ch. 10.6 - Find a route with the least total airfare that...Ch. 10.6 - Construct a weighted undirected graph such that...Ch. 10.6 - Show that the problem of finding a circuit of...Ch. 10.6 - The longest path problemin a weighted directed...Ch. 10.7 - Can five houses be connected to two utilities...Ch. 10.7 - In Exercises 2-4 draw the given planar graph...Ch. 10.7 - In Exercises 2-4 draw the given planar graph...Ch. 10.7 - In Exercises 2-4 draw the given planar graph...Ch. 10.7 - In Exercises 5-9 determine whether the given graph...Ch. 10.7 - In Exercises 5-9 determine whether the given graph...Ch. 10.7 - In Exercises 5-9 determine whether the given graph...Ch. 10.7 - In Exercises 5-9 determine whether the given graph...Ch. 10.7 - In Exercises 5-9 determine whether the given graph...Ch. 10.7 - Complete the argument inExample 3.Ch. 10.7 - Show thatK5is nonplanar using an argument similar...Ch. 10.7 - Prob. 12ECh. 10.7 - Prob. 13ECh. 10.7 - Prob. 14ECh. 10.7 - ProveCorollary 3.Ch. 10.7 - Prob. 16ECh. 10.7 - Prob. 17ECh. 10.7 - Suppose that a planar graph haskconnected...Ch. 10.7 - Which of these nonplanar graphs have the property...Ch. 10.7 - Prob. 20ECh. 10.7 - In Exercises 20-22 determine whether the given...Ch. 10.7 - Prob. 22ECh. 10.7 - Prob. 23ECh. 10.7 - Prob. 24ECh. 10.7 - Prob. 25ECh. 10.7 - Prob. 26ECh. 10.7 - Prob. 27ECh. 10.7 - Prob. 28ECh. 10.7 - Prob. 29ECh. 10.7 - Show thatK3,3has 2 as its thickness.Ch. 10.7 - Find the thickness of the graphs in Exercise 27.Ch. 10.7 - Show that ifGis a connected simple graph...Ch. 10.7 - Prob. 33ECh. 10.7 - Prob. 34ECh. 10.7 - Prob. 35ECh. 10.7 - Prob. 36ECh. 10.7 - Draw K3,3on the surface of a torus so that no...Ch. 10.8 - Prob. 1ECh. 10.8 - Prob. 2ECh. 10.8 - Prob. 3ECh. 10.8 - Prob. 4ECh. 10.8 - Prob. 5ECh. 10.8 - Prob. 6ECh. 10.8 - Prob. 7ECh. 10.8 - Prob. 8ECh. 10.8 - Prob. 9ECh. 10.8 - Prob. 10ECh. 10.8 - Prob. 11ECh. 10.8 - Prob. 12ECh. 10.8 - Prob. 13ECh. 10.8 - What is the least number of colors needed to color...Ch. 10.8 - Prob. 15ECh. 10.8 - Show that a simple graph that has a circuit with...Ch. 10.8 - Schedule the final exams for Math 115, Math 116,...Ch. 10.8 - How many different channels are needed for six...Ch. 10.8 - The mathematics department has six committees,...Ch. 10.8 - Prob. 20ECh. 10.8 - Find the edge chromatic number of each of the...Ch. 10.8 - Prob. 22ECh. 10.8 - Find the edge chromatic numbers of a)Cn,wheren3....Ch. 10.8 - Prob. 24ECh. 10.8 - Show that ifGis a graph withnvertices, there no...Ch. 10.8 - Find the edge chromatic number ofKnwhen n is a...Ch. 10.8 - Prob. 27ECh. 10.8 - Prob. 28ECh. 10.8 - Construct a coloring of the graph shown using this...Ch. 10.8 - Use pseudocode to describe this coloring...Ch. 10.8 - Show that the coloring produced by this algorithm...Ch. 10.8 - Show thatCnis chromatically 3-critical whenevernis...Ch. 10.8 - Show thatWnis chromatically 4-critical whenever n...Ch. 10.8 - Prob. 34ECh. 10.8 - Prob. 35ECh. 10.8 - Find these values: a)X2(K3) b)X2(K4) c) X2(W4)...Ch. 10.8 - Prob. 37ECh. 10.8 - Prob. 38ECh. 10.8 - Frequencies for mobile radio (or cellular)...Ch. 10.8 - Show that every planar graph G can be colored...Ch. 10.8 - Prob. 41ECh. 10.8 - Show that g(3) = 1 and g(4) = 1 by showing that...Ch. 10.8 - Show that g(5) = 1. That is, show that all...Ch. 10.8 - Show that g(6) = 2by first using Exercises 42 and...Ch. 10.8 - Prob. 45ECh. 10.8 - Solve the art gallery problem by proving theart...Ch. 10 - a) Define a simple graph, a multigraph, a...Ch. 10 - Prob. 2RQCh. 10 - What is the relationship between the sum of the...Ch. 10 - Why must there be an even number of vertices of...Ch. 10 - Prob. 5RQCh. 10 - Describe the following families of graphs....Ch. 10 - Prob. 7RQCh. 10 - Prob. 8RQCh. 10 - a) Describe three different methods that can be...Ch. 10 - a) What does it mean for two simple graphs to be...Ch. 10 - a) What does it mean for a graph to be connected?...Ch. 10 - Prob. 12RQCh. 10 - a) Define an Euler circuit and an Euler path in an...Ch. 10 - Prob. 14RQCh. 10 - Give examples of at least two problems that can be...Ch. 10 - a) Describe Dijkstra's algorithm for finding the...Ch. 10 - a) What does it mean for a graph to be planar? b)...Ch. 10 - a) What is Eider's formula for connected planar...Ch. 10 - Prob. 19RQCh. 10 - a) Define the chromatic number of a graph. b) What...Ch. 10 - Prob. 21RQCh. 10 - Prob. 22RQCh. 10 - Prob. 1SECh. 10 - How many nonisomorphic subgraphs doesK3have?Ch. 10 - Prob. 3SECh. 10 - Prob. 4SECh. 10 - Prob. 5SECh. 10 - Prob. 6SECh. 10 - Prob. 7SECh. 10 - Prob. 8SECh. 10 - LetG= (V, E)be an undirected graph and let...Ch. 10 - Prob. 10SECh. 10 - Prob. 11SECh. 10 - Prob. 12SECh. 10 - Prob. 13SECh. 10 - Prob. 14SECh. 10 - We say that three verticesu, v, andwof a simple...Ch. 10 - Find the clustering coefficient of each of the...Ch. 10 - Prob. 17SECh. 10 - For each of the graphs in Exercise 17, explain...Ch. 10 - Prob. 19SECh. 10 - A cliquein a simple undirected graph is a complete...Ch. 10 - Prob. 21SECh. 10 - Prob. 22SECh. 10 - Prob. 23SECh. 10 - Prob. 24SECh. 10 - Prob. 25SECh. 10 - Prob. 26SECh. 10 - A simple graph can be used to determine the...Ch. 10 - A simple graph can be used to determine the...Ch. 10 - A simple graph can be used to determine the...Ch. 10 - A simple graph can be used to determine the...Ch. 10 - Prob. 31SECh. 10 - A simple graph can be used to determine the...Ch. 10 - Prob. 33SECh. 10 - Prob. 34SECh. 10 - Prob. 35SECh. 10 - Prob. 36SECh. 10 - An orientationof an undirected simple graph is an...Ch. 10 - Prob. 38SECh. 10 - Prob. 39SECh. 10 - A tournament is a simple directed graph such that...Ch. 10 - Prob. 41SECh. 10 - A tournamentis a simple directed graph such that...Ch. 10 - Prob. 43SECh. 10 - Prob. 44SECh. 10 - Prob. 45SECh. 10 - Prob. 46SECh. 10 - A connected graphG = (V, E)withnvertices and m...Ch. 10 - A connected graphG = (V, E)withnvertices and m...Ch. 10 - Prob. 49SECh. 10 - Prob. 50SECh. 10 - Prob. 51SECh. 10 - Thedistancebetween two distinct verticesv1and v2of...Ch. 10 - a) Show that if the diameter of the simple graph G...Ch. 10 - Prob. 54SECh. 10 - Prob. 55SECh. 10 - Devise an algorithm for finding the second...Ch. 10 - Prob. 57SECh. 10 - Prob. 58SECh. 10 - Show that ifGis a simple graph with at least 11...Ch. 10 - Prob. 60SECh. 10 - Prob. 61SECh. 10 - Show that the chromatic number of a graph is less...Ch. 10 - Suppose that to generate a random simple graph...Ch. 10 - For each of these properties, determine whether it...Ch. 10 - Prob. 65SECh. 10 - Prob. 66SECh. 10 - Prob. 1CPCh. 10 - Prob. 2CPCh. 10 - Prob. 3CPCh. 10 - Prob. 4CPCh. 10 - Prob. 5CPCh. 10 - Prob. 6CPCh. 10 - Prob. 7CPCh. 10 - Prob. 8CPCh. 10 - Given, a positive integer n, generate a simple...Ch. 10 - Prob. 10CPCh. 10 - Prob. 11CPCh. 10 - Prob. 12CPCh. 10 - Given the vertex pairs associated to the edges of...Ch. 10 - Given the ordered pairs of vertices associated to...Ch. 10 - Given the list of edges of a simple graph, produce...Ch. 10 - Given the list of edges of a simple graph, produce...Ch. 10 - Given the list of edges and weights of these edges...Ch. 10 - Given the list of edges of an undirected graph,...Ch. 10 - Prob. 19CPCh. 10 - Given the distances between pairs of television...Ch. 10 - Prob. 1CAECh. 10 - Prob. 2CAECh. 10 - Prob. 3CAECh. 10 - Prob. 4CAECh. 10 - Prob. 5CAECh. 10 - Prob. 6CAECh. 10 - Prob. 7CAECh. 10 - Prob. 8CAECh. 10 - Generate at random simple graphs with 10 vertices....Ch. 10 - Generate at random simple graphs with 10 vertices....Ch. 10 - Find the chromatic number of each of the graphs...Ch. 10 - Find the shortest path a traveling salesperson can...Ch. 10 - Prob. 13CAECh. 10 - Prob. 14CAECh. 10 - Describe the origins and development of graph...Ch. 10 - Prob. 2WPCh. 10 - Discuss the applications of graph theory to...Ch. 10 - Prob. 4WPCh. 10 - Explain what community structure is in a graph...Ch. 10 - Describe some of the algorithms used to detect...Ch. 10 - Prob. 7WPCh. 10 - Explain how graph theory can help uncover networks...Ch. 10 - Prob. 9WPCh. 10 - Prob. 10WPCh. 10 - Prob. 11WPCh. 10 - Prob. 12WPCh. 10 - Describe how Euler paths can be used to help...Ch. 10 - Prob. 14WPCh. 10 - Describe theChinese postman problemand explain how...Ch. 10 - Describe some of the different conditions that...Ch. 10 - Prob. 17WPCh. 10 - Prob. 18WPCh. 10 - In modeling, very large scale integration (VLSI)...Ch. 10 - Prob. 20WPCh. 10 - Prob. 21WPCh. 10 - Describe and compare several different algorithms...Ch. 10 - Explain how graph multicolorings can be used in a...Ch. 10 - Prob. 24WPCh. 10 - Explain how the theory of random graphs can be...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- If during the following year it is predicted that each comedy skit will generate 30 thousand and each musical number 20 thousand, find the maximum income for the year. A television program director must schedule comedy skits and musical numbers for prime-time variety shows. Each comedy skit requires 2 hours of rehearsal time, costs 3000, and brings in 20,000 from the shows sponsors. Each musical number requires 1 hour of rehearsal time, costs 6000, and generates 12,000. If 250 hours are available for rehearsal and 600,000 is budgeted for comedy and music, how many segments of each type should be produced to maximize income? Find the maximum income.arrow_forwardPlease formulate the problem and solve it usingExcel Solver!arrow_forwardA businesswoman wants to determine the difference between the costs of owning and leasing an automobile. She can lease a car for $440 a per month (on an annual basis). Under this plan, the cost per mile is $0.07. If she were to purchase the car, the fixed annual expense would be $4800, and other costs would amount to $0.11 per mile. What is the least number of miles she would have to drive per year to make leasing no more expensive than purchasing? The businesswoman would have to drive at least miles per year.arrow_forward
- Task C has two immediate predecessors, tasks A and B. Task A has an early finish time of 3 days, and task B has an early finish time of 5 days. Task C is 2 days long. What is the early finish time of task C?arrow_forwardA carpenter builds bookshelves and tables for a living. Each bookshelf takes one box of screws, two 2 ✕ 4's, and three sheets of plywood to make. Each table takes two boxes of screws, two 2 ✕ 4's, and four sheets of plywood. The carpenter has 55 boxes of screws, 70 2 ✕ 4's, and 115 sheets of plywood on hand. In order to maximize their profit using these materials on hand, the carpenter has determined that they must build 10 shelves and 20 tables. How many of each of the materials (boxes of screws, 2 ✕ 4's, and sheets of plywood) are leftover, when the carpenter builds 10 shelves and 20 tables? The carpenter has _ boxes of screws, _ 2 ✕ 4's, and _ sheets of plywood leftover.arrow_forwardA carpenter builds bookshelves and tables for a living. Each bookshelf takes one box of screws, two 2 ✕ 4's, and three sheets of plywood to make. Each table takes two boxes of screws, four 2 ✕ 4's, and four sheets of plywood. The carpenter has 80 boxes of screws, 145 2 ✕ 4's, and 170 sheets of plywood on hand. In order to maximize their profit using these materials on hand, the carpenter has determined that they must build 12 shelves and 29 tables. How many of each of the materials (boxes of screws, 2 ✕ 4's, and sheets of plywood) are leftover, when the carpenter builds 12 shelves and 29 tables? The carpenter has boxes of screws, 2 ✕ 4's, and sheets of plywood leftover.arrow_forward
- Giovanni Food Products produces and sells frozen pizzas to public schools throughout the eastern United States. Using a very aggressive marketing strategy they have been able to increase their annual revenue by approximately $10 million over the past 10 years. But increased competition has slowed their growth rate in the past few years. The annual revenue, in millions of dollars, for the previous 10 years is contained in the Excel Online file below. Construct a spreadsheet to answer the following questions.arrow_forwardSolve step by step in digital format 3. Graph and conclude according to the variable under study, productions were taken in tons of corn, sorghum and beans in three different regions of the country and the following was found in the northern zone: 500, 400, 200, respectively, for the central region the following 700,500,500 were found and for the southern region the following 1000,700,300.arrow_forwardPROBLEM 03: The Jokia Cell Phone Company manufactures two models of cell phones - the Wombat and the Sloth. Each Wombat phone uses 2.5 ounces of gold leaf and 3 ounces of plastic, whereas each Sloth phone uses 2 ounces of gold leaf and 2 ounces of plastic. Each day, the company has only 370 ounces of gold leaf and 420 ounces of plastic to be used for making cell phones. If the company makes the correct number of each type of phone on a given day to use up all of the available gold leaf and plastic, how many Wombat phones will be made? A) 60 B) 100 C) 50 D) 90 E) 110 N) none of the abovearrow_forward
- Use simplex methodarrow_forwardExplain four components of a research problemarrow_forwardA plumbing repair company has 3 employees and must choose which of 3 jobs to assign each to (each employee is assigned to exactly one job and each job must have someone assigned). Each employee can perform each job, but the cost to perform any given job can vary. The following table shows the cost for each employee to perform each job. Employee A Employee B Employee C Job 1 48 45 44 Job 2 43 35 45 Job 3 51 51 50 Solve this assignment problem in Excel to find the lowest cost solution and answer the following questions: a. Which employee is assigned to job 1? (Click to select) ♥ b. Which employee is assigned to job 2? (Click to select) ♥ c. Which employee is assigned to job 3? (Click to select) ♥ d. What is the minimum cost to complete all three jobs? Minimum costarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Algebra for College StudentsAlgebraISBN:9781285195780Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage Learning
Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Algebra for College Students
Algebra
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Cengage Learning
Elementary Geometry for College Students
Geometry
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Cengage Learning