DISCRETE MATHEMATICS+ITS APPL. (LL)-W/A
8th Edition
ISBN: 9781260521337
Author: ROSEN
Publisher: MCG
expand_more
expand_more
format_list_bulleted
Question
Chapter 11.5, Problem 19E
To determine
To show:
There is a unique spanning tree in a connected weighted graph is the weights of the edges are all different.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Give an example of a graph which has precisely seven (possibly isomorphic) minimum spanning trees.
Give a simple example of a connected graph such that an edge (u, v) is a light edge for some cut, but there exists a minimum spanning tree that does not contain (u, v).
Question8. Find a spanning tree of minimum weight for the graph weighted G.
Chapter 11 Solutions
DISCRETE MATHEMATICS+ITS APPL. (LL)-W/A
Ch. 11.1 - Prob. 1ECh. 11.1 - Vhich of these graphs are trees?Ch. 11.1 - Prob. 3ECh. 11.1 - Prob. 4ECh. 11.1 - Prob. 5ECh. 11.1 - Prob. 6ECh. 11.1 - Prob. 7ECh. 11.1 - Prob. 8ECh. 11.1 - Prob. 9ECh. 11.1 - Prob. 10E
Ch. 11.1 - Prob. 11ECh. 11.1 - Prob. 12ECh. 11.1 - Prob. 13ECh. 11.1 - Prob. 14ECh. 11.1 - Let G he a simple graph with n vertices. Show that...Ch. 11.1 - Prob. 16ECh. 11.1 - Prob. 17ECh. 11.1 - Prob. 18ECh. 11.1 - Prob. 19ECh. 11.1 - Prob. 20ECh. 11.1 - Prob. 21ECh. 11.1 - A chain letter starts when a person sends a letter...Ch. 11.1 - A chain letter starts with a person sending a...Ch. 11.1 - Prob. 24ECh. 11.1 - Prob. 25ECh. 11.1 - Prob. 26ECh. 11.1 - Prob. 27ECh. 11.1 - Prob. 28ECh. 11.1 - Prob. 29ECh. 11.1 - Prob. 30ECh. 11.1 - Prob. 31ECh. 11.1 - Prob. 32ECh. 11.1 - Prob. 33ECh. 11.1 - Prob. 34ECh. 11.1 - Prob. 35ECh. 11.1 - Prob. 36ECh. 11.1 - Letnbe a power of 2. Show thatnnumbers can be...Ch. 11.1 - Prob. 38ECh. 11.1 - Prob. 39ECh. 11.1 - Prob. 40ECh. 11.1 - Prob. 41ECh. 11.1 - Prob. 42ECh. 11.1 - Prob. 43ECh. 11.1 - Prob. 44ECh. 11.1 - Draw the first seven rooted Fibonacci trees.Ch. 11.1 - Prob. 46ECh. 11.1 - Prob. 47ECh. 11.1 - Show that the average depth of a leaf in a binary...Ch. 11.2 - Build a binary search tree for the...Ch. 11.2 - Build a binary search tree for the words oenology,...Ch. 11.2 - How many comparisons are needed to locate or to...Ch. 11.2 - How many comparisons are needed to locate or to...Ch. 11.2 - Using alphabetical order, construct a binary...Ch. 11.2 - How many weighings of a balance scale are needed...Ch. 11.2 - How many weighings of a balance scale are needed...Ch. 11.2 - How many weighings of a balance scale are needed...Ch. 11.2 - How many weighings of a balance scale are needed...Ch. 11.2 - One of four coins may be counterfeit. If it is...Ch. 11.2 - Find the least number of comparisons needed to...Ch. 11.2 - Prob. 12ECh. 11.2 - The tournament sort is a sorting algorithm that...Ch. 11.2 - The tournament sort is a sorting algorithm that...Ch. 11.2 - Prob. 15ECh. 11.2 - Prob. 16ECh. 11.2 - Prob. 17ECh. 11.2 - The tournament sort is a sorting algorithm that...Ch. 11.2 - The tournament sort is a sorting algorithm that...Ch. 11.2 - The tournament sort is a sorting algorithm that...Ch. 11.2 - Prob. 21ECh. 11.2 - The tournament sort is a sorting algorithm that...Ch. 11.2 - Prob. 23ECh. 11.2 - The tournament sort is a sorting algorithm that...Ch. 11.2 - Prob. 25ECh. 11.2 - The tournament sort is a sorting algorithm that...Ch. 11.2 - Prob. 27ECh. 11.2 - Prob. 28ECh. 11.2 - Suppose thatmis a positive integer with m>2An...Ch. 11.2 - Suppose that m is a positive integer with m>2 An...Ch. 11.2 - Suppose that m is a positive integer withm= 2. An...Ch. 11.2 - Suppose thatmis a positive integer withm= 2....Ch. 11.2 - Prob. 33ECh. 11.2 - Prob. 34ECh. 11.2 - Suppose that m is a positive integer with m>2 An...Ch. 11.2 - Prob. 36ECh. 11.2 - Suppose that m is a positive integer with m>2 An...Ch. 11.2 - Suppose that m is a positive integer with m>2 An...Ch. 11.2 - Prob. 39ECh. 11.2 - Suppose that m is a positive integer withm= 2. An...Ch. 11.2 - Prob. 41ECh. 11.2 - Suppose that m is a positive integer with m>2 An...Ch. 11.2 - Prob. 43ECh. 11.2 - Prob. 44ECh. 11.3 - Prob. 1ECh. 11.3 - Prob. 2ECh. 11.3 - Prob. 3ECh. 11.3 - Prob. 4ECh. 11.3 - Suppose that the vertex with the largest address...Ch. 11.3 - Prob. 6ECh. 11.3 - Prob. 7ECh. 11.3 - Prob. 8ECh. 11.3 - Prob. 9ECh. 11.3 - Prob. 10ECh. 11.3 - Prob. 11ECh. 11.3 - Prob. 12ECh. 11.3 - Prob. 13ECh. 11.3 - Prob. 14ECh. 11.3 - Prob. 15ECh. 11.3 - Prob. 16ECh. 11.3 - Prob. 17ECh. 11.3 - a) Represent the compound propositionsandusing...Ch. 11.3 - a) Represent(AB)(A(BA))using an ordered rooted...Ch. 11.3 - In how many ways can the stringbe fully...Ch. 11.3 - In how many ways can the stringbe fully...Ch. 11.3 - Draw the ordered rooted tree corresponding to each...Ch. 11.3 - What is the value of each of these prefix...Ch. 11.3 - What is the value of each of these postfix...Ch. 11.3 - Prob. 25ECh. 11.3 - Prob. 26ECh. 11.3 - Prob. 27ECh. 11.3 - Prob. 28ECh. 11.3 - Prob. 29ECh. 11.3 - Prob. 30ECh. 11.3 - Show that any well-formed formula in prefix...Ch. 11.3 - Prob. 32ECh. 11.3 - Prob. 33ECh. 11.3 - Prob. 34ECh. 11.4 - How many edges must be removed from a connected...Ch. 11.4 - Prob. 2ECh. 11.4 - Prob. 3ECh. 11.4 - Prob. 4ECh. 11.4 - Prob. 5ECh. 11.4 - Prob. 6ECh. 11.4 - Prob. 7ECh. 11.4 - Prob. 8ECh. 11.4 - Prob. 9ECh. 11.4 - Prob. 10ECh. 11.4 - Prob. 11ECh. 11.4 - Prob. 12ECh. 11.4 - Prob. 13ECh. 11.4 - Prob. 14ECh. 11.4 - Prob. 15ECh. 11.4 - Prob. 16ECh. 11.4 - Prob. 17ECh. 11.4 - Prob. 18ECh. 11.4 - Prob. 19ECh. 11.4 - Prob. 20ECh. 11.4 - Prob. 21ECh. 11.4 - Describe the tree produced by breadth-first search...Ch. 11.4 - Prob. 23ECh. 11.4 - Explain how breadth-first search or depth-first...Ch. 11.4 - Prob. 25ECh. 11.4 - Prob. 26ECh. 11.4 - Prob. 27ECh. 11.4 - Use backtracking to find a subset, if it exists,...Ch. 11.4 - Explain how backtracking can be used to find a...Ch. 11.4 - Prob. 30ECh. 11.4 - Prob. 31ECh. 11.4 - A spanning forest of a graphGis a forest that...Ch. 11.4 - Prob. 33ECh. 11.4 - Prob. 34ECh. 11.4 - Prob. 35ECh. 11.4 - A spanning forest of a graphGis a forest that...Ch. 11.4 - Prob. 37ECh. 11.4 - Prob. 38ECh. 11.4 - Prob. 39ECh. 11.4 - Prob. 40ECh. 11.4 - Prob. 41ECh. 11.4 - Prob. 42ECh. 11.4 - Prob. 43ECh. 11.4 - Prob. 44ECh. 11.4 - Prob. 45ECh. 11.4 - Prob. 46ECh. 11.4 - Prob. 47ECh. 11.4 - Prob. 48ECh. 11.4 - Prob. 49ECh. 11.4 - Prob. 50ECh. 11.4 - Prob. 51ECh. 11.4 - Prob. 52ECh. 11.4 - Prob. 53ECh. 11.4 - Prob. 54ECh. 11.4 - Prob. 55ECh. 11.4 - Prob. 56ECh. 11.4 - Prob. 57ECh. 11.4 - Prob. 58ECh. 11.4 - Prob. 59ECh. 11.4 - Prob. 60ECh. 11.4 - Prob. 61ECh. 11.5 - The roads represented by this graph are all...Ch. 11.5 - Prob. 2ECh. 11.5 - Prob. 3ECh. 11.5 - Prob. 4ECh. 11.5 - Prob. 5ECh. 11.5 - Prob. 6ECh. 11.5 - Prob. 7ECh. 11.5 - Prob. 8ECh. 11.5 - Prob. 9ECh. 11.5 - Prob. 10ECh. 11.5 - Prob. 11ECh. 11.5 - Prob. 12ECh. 11.5 - Prob. 13ECh. 11.5 - Prob. 14ECh. 11.5 - Prob. 15ECh. 11.5 - Prob. 16ECh. 11.5 - Prob. 17ECh. 11.5 - Prob. 18ECh. 11.5 - Prob. 19ECh. 11.5 - Prob. 20ECh. 11.5 - Prob. 21ECh. 11.5 - Prob. 22ECh. 11.5 - Express the algorithm devised in Exercise 22 in...Ch. 11.5 - Prob. 24ECh. 11.5 - Prob. 25ECh. 11.5 - Prob. 26ECh. 11.5 - Prob. 27ECh. 11.5 - Prob. 28ECh. 11.5 - Prob. 29ECh. 11.5 - Prob. 30ECh. 11.5 - Prob. 31ECh. 11.5 - Prob. 32ECh. 11.5 - Prob. 33ECh. 11.5 - Prob. 34ECh. 11.5 - Prob. 35ECh. 11 - Prob. 1RQCh. 11 - Prob. 2RQCh. 11 - Prob. 3RQCh. 11 - Prob. 4RQCh. 11 - Prob. 5RQCh. 11 - Prob. 6RQCh. 11 - Prob. 7RQCh. 11 - a) What is a binary search tree? b) Describe an...Ch. 11 - Prob. 9RQCh. 11 - Prob. 10RQCh. 11 - a) Explain how to use preorder, inorder, and...Ch. 11 - Show that the number of comparisons used by a...Ch. 11 - a) Describe the Huffman coding algorithm for...Ch. 11 - Draw the game tree for nim if the starting...Ch. 11 - Prob. 15RQCh. 11 - Prob. 16RQCh. 11 - a) Explain how backtracking can be used to...Ch. 11 - Prob. 18RQCh. 11 - Prob. 19RQCh. 11 - Show that a simple graph is a tree if and Only if...Ch. 11 - Prob. 2SECh. 11 - Prob. 3SECh. 11 - Prob. 4SECh. 11 - Prob. 5SECh. 11 - Prob. 6SECh. 11 - Prob. 7SECh. 11 - Prob. 8SECh. 11 - Prob. 9SECh. 11 - Prob. 10SECh. 11 - Prob. 11SECh. 11 - Prob. 12SECh. 11 - Prob. 13SECh. 11 - Prob. 14SECh. 11 - Prob. 15SECh. 11 - Prob. 16SECh. 11 - Prob. 17SECh. 11 - Prob. 18SECh. 11 - Prob. 19SECh. 11 - Prob. 20SECh. 11 - Prob. 21SECh. 11 - Prob. 22SECh. 11 - Prob. 23SECh. 11 - The listing of the vertices of an ordered rooted...Ch. 11 - The listing of the vertices of an ordered rooted...Ch. 11 - Prob. 26SECh. 11 - Prob. 27SECh. 11 - Prob. 28SECh. 11 - Prob. 29SECh. 11 - Show that if every circuit not passing through any...Ch. 11 - Prob. 31SECh. 11 - Prob. 32SECh. 11 - Prob. 33SECh. 11 - Prob. 34SECh. 11 - Prob. 35SECh. 11 - Prob. 36SECh. 11 - Prob. 37SECh. 11 - Prob. 38SECh. 11 - Prob. 39SECh. 11 - Prob. 40SECh. 11 - Prob. 41SECh. 11 - Prob. 42SECh. 11 - Prob. 43SECh. 11 - Prob. 44SECh. 11 - Prob. 45SECh. 11 - Show that a directed graphG= (V,E) has an...Ch. 11 - In this exercise we will develop an algorithm to...Ch. 11 - Prob. 1CPCh. 11 - Prob. 2CPCh. 11 - Prob. 3CPCh. 11 - Prob. 4CPCh. 11 - Prob. 5CPCh. 11 - Prob. 6CPCh. 11 - Prob. 7CPCh. 11 - Given an arithmetic expression in prefix form,...Ch. 11 - Prob. 9CPCh. 11 - Given the frequency of symbols, use Huffman coding...Ch. 11 - Given an initial position in the game of nim,...Ch. 11 - Prob. 12CPCh. 11 - Prob. 13CPCh. 11 - Prob. 14CPCh. 11 - Prob. 15CPCh. 11 - Prob. 16CPCh. 11 - Prob. 17CPCh. 11 - Prob. 18CPCh. 11 - Prob. 1CAECh. 11 - Prob. 2CAECh. 11 - Prob. 3CAECh. 11 - Prob. 4CAECh. 11 - Prob. 5CAECh. 11 - Prob. 6CAECh. 11 - Prob. 7CAECh. 11 - Prob. 8CAECh. 11 - Prob. 1WPCh. 11 - Prob. 2WPCh. 11 - Prob. 3WPCh. 11 - DefineAVL-trees(sometimes also known...Ch. 11 - Prob. 5WPCh. 11 - Prob. 6WPCh. 11 - Prob. 7WPCh. 11 - Prob. 8WPCh. 11 - Prob. 9WPCh. 11 - Prob. 10WPCh. 11 - Discuss the algorithms used in IP multicasting to...Ch. 11 - Prob. 12WPCh. 11 - Describe an algorithm based on depth-first search...Ch. 11 - Prob. 14WPCh. 11 - Prob. 15WPCh. 11 - Prob. 16WPCh. 11 - Prob. 17WPCh. 11 - Prob. 18WP
Knowledge Booster
Similar questions
- Show that a finite simple graph with more than one vertex has at least two vertices with the same degree.arrow_forwardUse the pigeonhole principle to prove that a graph has at least two vertices with the same degreearrow_forwardI have a graph with 2021 vertices. It is not a tree but there exists some vertex whose removal makes it a tree. What is the maximum possible number of edges in the original graph?arrow_forward
- A school consists of 6 separate buildings, represented by the vertices in the graph. There are paths between some of the buildings as shown. The graph also shows the length in feet of each path. School administrators want to cover some of these paths with roofs so that students will be able to walk between buildings without getting wet when it rains. To minimize cost, they must select paths to be covered such that the total length to be covered is as small as possible. Use Kruskal's algorithm to determine which paths to cover. Also determine the total length of pathways to be covered. OA. Click here to view figure c. OC. Click here to view figure b. A The total length of pathways to be covered is (Type a whole number.) 45 B Find a minimum spanning tree. Choose the correct answer below. 51 34 19 39 25 E 31 29 30 25 F41 (... D 35 O B. Click here to view figure d. O D. Click here to view figure a.arrow_forwardIf using Prim's algorithm, what is the total weight of the minimum spanning tree of the following graph: PLEASE HELP SIR, THX.arrow_forwardShow that the maximum number of edges in a graph with n-vertices is *C2 (d)arrow_forward
- le bus zzes dules BlueButton aborations iopto Vidco What is the minimum number of edges for a spanning tree for this graph?arrow_forwardThe definition of weighted graph is such that every edge has positive weight. If the def- inition was changed to permit negative (or zero) weights, would Kruskal's and Dijkstra's algorithms continue to work? Give a proof or counterexample in each case.arrow_forward(a) Explain briefly the Minimal Spanning Tree Algorithm (Kruskal). Refer to the selecting procedure of edges as well as the stopping condition of the algorithm.arrow_forward
- What is the least possible number of edges in a graph with 7 vertices in which every edge is in at least two cycles? Draw an example of such a graph with this number of edges.arrow_forwardLet (u, v) be a minimum-weight edge in a connected graph G. Show that (u, v) belongs to some minimum spanning tree of G.arrow_forwardExplain the step by step procedure of Dijktra’s algorithm to find the shortest path between any two vertices?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill Education
Mathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSON
Discrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,
Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education
Discrete Mathematics and Its Applications ( 8th I...
Math
ISBN:9781259676512
Author:Kenneth H Rosen
Publisher:McGraw-Hill Education
Mathematics for Elementary Teachers with Activiti...
Math
ISBN:9780134392790
Author:Beckmann, Sybilla
Publisher:PEARSON
Thinking Mathematically (7th Edition)
Math
ISBN:9780134683713
Author:Robert F. Blitzer
Publisher:PEARSON
Discrete Mathematics With Applications
Math
ISBN:9781337694193
Author:EPP, Susanna S.
Publisher:Cengage Learning,
Pathways To Math Literacy (looseleaf)
Math
ISBN:9781259985607
Author:David Sobecki Professor, Brian A. Mercer
Publisher:McGraw-Hill Education