Discrete Mathematics With Applications
5th Edition
ISBN: 9780357035283
Author: EPP
Publisher: Cengage
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Chapter 10.4, Problem 26ES
If a graph has n vertices and
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For each of the time series, construct a line chart of the data and identify the characteristics of the time series (that is, random, stationary, trend, seasonal, or cyclical).
Month Number (Thousands)Dec 1991 65.60Jan 1992 71.60Feb 1992 78.80Mar 1992 111.60Apr 1992 107.60May 1992 115.20Jun 1992 117.80Jul 1992 106.20Aug 1992 109.90Sep 1992 106.00Oct 1992 111.80Nov 1992 84.50Dec 1992 78.60Jan 1993 70.50Feb 1993 74.60Mar 1993 95.50Apr 1993 117.80May 1993 120.90Jun 1993 128.50Jul 1993 115.30Aug 1993 121.80Sep 1993 118.50Oct 1993 123.30Nov 1993 102.30Dec 1993 98.70Jan 1994 76.20Feb 1994 83.50Mar 1994 134.30Apr 1994 137.60May 1994 148.80Jun 1994 136.40Jul 1994 127.80Aug 1994 139.80Sep 1994 130.10Oct 1994 130.60Nov 1994 113.40Dec 1994 98.50Jan 1995 84.50Feb 1995 81.60Mar 1995 103.80Apr 1995 116.90May 1995 130.50Jun 1995 123.40Jul 1995 129.10Aug 1995…
Chapter 10 Solutions
Discrete Mathematics With Applications
Ch. 10.1 - Let G be a graph and let v and w be vertices in G....Ch. 10.1 - A graph is connected if, any only if, _____.Ch. 10.1 - Removing an edge from a circuit in a graph does...Ch. 10.1 - An Euler circuit in graph is _____.Ch. 10.1 - Prob. 5TYCh. 10.1 - Prob. 6TYCh. 10.1 - Prob. 7TYCh. 10.1 - If a graph G has a Hamiltonian circuit, then G has...Ch. 10.1 - A travelling salesman problem involves finding a...Ch. 10.1 - In the graph below, determine whether the...
Ch. 10.1 - In the graph below, determine whether the...Ch. 10.1 - Let G be the graph and consider the walk...Ch. 10.1 - Consider the following graph. How many paths are...Ch. 10.1 - Consider the following graph. How many paths are...Ch. 10.1 - An edge whose removal disconnects the graph of...Ch. 10.1 - Given any positive integer n, (a) find a connected...Ch. 10.1 - Find the number of connected components for each...Ch. 10.1 - Each of (a)—(c) describes a graph. In each case...Ch. 10.1 - Prob. 10ESCh. 10.1 - Is it possible for a citizen of Königsberg to make...Ch. 10.1 - Determine which of the graph in 12-17 have Euler...Ch. 10.1 - Determine which of the graph in 12-17 have Euler...Ch. 10.1 - Determine which of the graph in 12-17 have Euler...Ch. 10.1 - Determine which of the graph in 12-17 have Euler...Ch. 10.1 - Determine which of the graph in 12-17 have Euler...Ch. 10.1 - Determine which of the graph in 12-17 have Euler...Ch. 10.1 - Is it possible to take a walk around the city...Ch. 10.1 - For each of the graph in 19-21, determine whether...Ch. 10.1 - Prob. 20ESCh. 10.1 - Prob. 21ESCh. 10.1 - Prob. 22ESCh. 10.1 - Prob. 23ESCh. 10.1 - Find the complement of each of the following...Ch. 10.1 - Find the complement of the graph K4, the complete...Ch. 10.1 - Suppose that in a group of five people A,B,C,D,...Ch. 10.1 - Prob. 27ESCh. 10.1 - Show that at a party with at least two people,...Ch. 10.1 - Find Hamiltonian circuits for each of the graph in...Ch. 10.1 - Find Hamiltonian circuits for each of the graph in...Ch. 10.1 - Prob. 31ESCh. 10.1 - Show that none of graphs in 31-33 has a...Ch. 10.1 - Prob. 33ESCh. 10.1 - Prob. 34ESCh. 10.1 - Prob. 35ESCh. 10.1 - In 34-37, find Hamiltonian circuits for those...Ch. 10.1 - Prob. 37ESCh. 10.1 - Give two examples of graphs that have Euler...Ch. 10.1 - Prob. 39ESCh. 10.1 - Prob. 40ESCh. 10.1 - Give two examples of graphs that have Euler...Ch. 10.1 - A traveler in Europe wants to visit each of the...Ch. 10.1 - a. Prove that if a walk in a graph contains a...Ch. 10.1 - Prob. 44ESCh. 10.1 - Prob. 45ESCh. 10.1 - Prob. 46ESCh. 10.1 - Prove that if there is a trail in a graph G from a...Ch. 10.1 - If a graph contains a circuits that starts and...Ch. 10.1 - Prob. 49ESCh. 10.1 - Let G be a connected graph, and let C be any...Ch. 10.1 - Prob. 51ESCh. 10.1 - Prob. 52ESCh. 10.1 - For what values of n dies the complete graph Kn...Ch. 10.1 - For what values of m and n does the complete...Ch. 10.1 - What is the maximum number of edges a simple...Ch. 10.1 - Prob. 56ESCh. 10.1 - Prob. 57ESCh. 10.2 - In the adjacency matrix for a directed graph, the...Ch. 10.2 - Prob. 2TYCh. 10.2 - Prob. 3TYCh. 10.2 - Prob. 4TYCh. 10.2 - Prob. 5TYCh. 10.2 - Prob. 6TYCh. 10.2 - Find real numbers a, b, and c such that the...Ch. 10.2 - Find the adjacency matrices for the following...Ch. 10.2 - Find directed graphs that have the following...Ch. 10.2 - Find adjacency matrices for the following...Ch. 10.2 - Find graphs that have the following adjacency...Ch. 10.2 - Prob. 6ESCh. 10.2 - Prob. 7ESCh. 10.2 - Prob. 8ESCh. 10.2 - Prob. 9ESCh. 10.2 - Prob. 10ESCh. 10.2 - Prob. 11ESCh. 10.2 - Prob. 12ESCh. 10.2 - Let O denote the matrix [0000] . Find 2 × 2...Ch. 10.2 - Prob. 14ESCh. 10.2 - Prob. 15ESCh. 10.2 - In 14-18, assume the entries of all matrices are...Ch. 10.2 - Prob. 17ESCh. 10.2 - Prob. 18ESCh. 10.2 - Prob. 19ESCh. 10.2 - The following is an adjacency matrix for a graph:...Ch. 10.2 - Let A be the adjacency matrix for K3, the complete...Ch. 10.2 - Draw a graph that has [0001200011000211120021100]...Ch. 10.2 - Prob. 23ESCh. 10.3 - If G and G’ are graphs, then G is isomorphic to G’...Ch. 10.3 - A property P is an invariant for graph isomorphism...Ch. 10.3 - Prob. 3TYCh. 10.3 - For each pair of graphs G and G’ in 1-5, determine...Ch. 10.3 - For each pair of graphs G and G’ in 1-5, determine...Ch. 10.3 - For each pair of graphs G and G’ in 1-5, determine...Ch. 10.3 - For each pair of graphs G and G’ in 1-5, determine...Ch. 10.3 - For each pair of graphs G and G in 1—5, determine...Ch. 10.3 - For each pair of graphs G and G’ in 6-13,...Ch. 10.3 - For each pair of graphs G and G’ in 6-13,...Ch. 10.3 - For each pair of graphs G and G’ in 6-13,...Ch. 10.3 - Prob. 9ESCh. 10.3 - For each pair of graphs G and G’ in 6-13,...Ch. 10.3 - For each pair of graphs G and G’ in 6-13,...Ch. 10.3 - For each pair of simple graphs G and G in 6—13,...Ch. 10.3 - For each pair of graphs G and G’ in 6-13,...Ch. 10.3 - Draw all nonisomorphic simple graphs with three...Ch. 10.3 - Draw all nonisomorphic simple graphs with four...Ch. 10.3 - Prob. 16ESCh. 10.3 - Draw all nonisomorphic graphs with four vertices...Ch. 10.3 - Draw all nonisomorphic graphs with four vertices...Ch. 10.3 - Prob. 19ESCh. 10.3 - Draw four nonisomorphic graphs with six vertices,...Ch. 10.3 - Prob. 21ESCh. 10.3 - Prove that each of the properties in 21-29 is an...Ch. 10.3 - Prob. 23ESCh. 10.3 - Prove that each of the properties in 21-29 is an...Ch. 10.3 - Prob. 25ESCh. 10.3 - Prob. 26ESCh. 10.3 - Prob. 27ESCh. 10.3 - Prove that each of the properties in 21-29 is an...Ch. 10.3 - Prob. 29ESCh. 10.3 - Show that the following two graphs are not...Ch. 10.4 - A circuit-free graph is a graph with __________.Ch. 10.4 - Prob. 2TYCh. 10.4 - Prob. 3TYCh. 10.4 - Prob. 4TYCh. 10.4 - Prob. 5TYCh. 10.4 - Prob. 6TYCh. 10.4 - For any positive integer n, if G is a connected...Ch. 10.4 - Read the tree in Example 10.4.2 from left to right...Ch. 10.4 - Prob. 2ESCh. 10.4 - Prob. 3ESCh. 10.4 - Prob. 4ESCh. 10.4 - Prob. 5ESCh. 10.4 - Prob. 6ESCh. 10.4 - Prob. 7ESCh. 10.4 - In each of 8—21, either draw a graph with the...Ch. 10.4 - In each of 8—21, either draw a graph with the...Ch. 10.4 - In each of 8—21, either draw a graph with the...Ch. 10.4 - In each of 8—21, either draw a graph with the...Ch. 10.4 - In each of 8—21, either draw a graph with the...Ch. 10.4 - In each of 8—21, either draw a graph with the...Ch. 10.4 - Prob. 14ESCh. 10.4 - In each of 8—21, either draw a graph with the...Ch. 10.4 - In each of 8—21, either draw a graph with the...Ch. 10.4 - Prob. 17ESCh. 10.4 - In each of 8—21, either draw a graph with the...Ch. 10.4 - In each of 8—21, either draw a graph with the...Ch. 10.4 - In each of 8—21, either draw a graph with the...Ch. 10.4 - In each of 8—21, either draw a graph with the...Ch. 10.4 - A connected graph has twelve vertices and eleven...Ch. 10.4 - A connected graph has nine vertices and twelve...Ch. 10.4 - Prob. 24ESCh. 10.4 - Prob. 25ESCh. 10.4 - If a graph has n vertices and n2 or fewer can it...Ch. 10.4 - A circuit-free graph has ten vertices and nine...Ch. 10.4 - Is a circuit-free graph with n vertices and at...Ch. 10.4 - Prob. 29ESCh. 10.4 - Prob. 30ESCh. 10.4 - a. Prove that the following is an invariant for...Ch. 10.5 - Prob. 1TYCh. 10.5 - Prob. 2TYCh. 10.5 - Prob. 3TYCh. 10.5 - Prob. 4TYCh. 10.5 - Prob. 5TYCh. 10.5 - Prob. 1ESCh. 10.5 - Prob. 2ESCh. 10.5 - Draw binary trees to represent the following...Ch. 10.5 - Prob. 4ESCh. 10.5 - Prob. 5ESCh. 10.5 - Prob. 6ESCh. 10.5 - Prob. 7ESCh. 10.5 - Prob. 8ESCh. 10.5 - Prob. 9ESCh. 10.5 - Prob. 10ESCh. 10.5 - Prob. 11ESCh. 10.5 - Prob. 12ESCh. 10.5 - Prob. 13ESCh. 10.5 - Prob. 14ESCh. 10.5 - Prob. 15ESCh. 10.5 - Prob. 16ESCh. 10.5 - Prob. 17ESCh. 10.5 - Prob. 18ESCh. 10.5 - Prob. 19ESCh. 10.5 - Prob. 20ESCh. 10.5 - Prob. 21ESCh. 10.5 - Prob. 22ESCh. 10.5 - Prob. 23ESCh. 10.5 - Prob. 24ESCh. 10.5 - In 21-25, use the steps of Algorithm 10.5.1 to...Ch. 10.6 - Prob. 1TYCh. 10.6 - Prob. 2TYCh. 10.6 - Prob. 3TYCh. 10.6 - In Kruskal’s algorithm, the edges of a connected,...Ch. 10.6 - Prob. 5TYCh. 10.6 - Prob. 6TYCh. 10.6 - At each stage of Dijkstra’s algorithm, the vertex...Ch. 10.6 - Prob. 1ESCh. 10.6 - Prob. 2ESCh. 10.6 - Prob. 3ESCh. 10.6 - Prob. 4ESCh. 10.6 - Prob. 5ESCh. 10.6 - Prob. 6ESCh. 10.6 - Prob. 7ESCh. 10.6 - Prob. 8ESCh. 10.6 - Prob. 9ESCh. 10.6 - Prob. 10ESCh. 10.6 - A pipeline is to be built that will link six...Ch. 10.6 - Use Dijkstra’s algorithm for the airline route...Ch. 10.6 - Use Dijkstra’s algorithm to find the shortest path...Ch. 10.6 - Use Dijkstra’s algorithm to find the shortest path...Ch. 10.6 - Use Dijkstra’s algorithm to find the shortest path...Ch. 10.6 - Use Dijkstra’s algorithm to find the shortest path...Ch. 10.6 - Prob. 17ESCh. 10.6 - Prob. 18ESCh. 10.6 - Prob. 19ESCh. 10.6 - Prob. 20ESCh. 10.6 - Prob. 21ESCh. 10.6 - Prob. 22ESCh. 10.6 - Prob. 23ESCh. 10.6 - Prob. 24ESCh. 10.6 - Prob. 25ESCh. 10.6 - Prob. 26ESCh. 10.6 - Prob. 27ESCh. 10.6 - Suppose a disconnected graph is input to Kruskal’s...Ch. 10.6 - Suppose a disconnected graph is input to Prim’s...Ch. 10.6 - Modify Algorithm 10.6.3 so that the output...Ch. 10.6 - Prob. 31ES
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