The Heart of Mathematics: An Invitation to Effective Thinking

4th Edition

ISBN: 9781118156599

Author: Edward B. Burger, Michael Starbird

Publisher: Wiley, John & Sons, Incorporated

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Chapter 6.4, Problem 8MS

Campus shortcut. Find a map of your campus and create a graph model that shows the main buildings or other locations you visit regularly. Each location is a vertex, with an edge between two vertices for which there is an easy campus route between the locations that doesn’t pass through a third location. If one of the vertices is your dorm, find a shortest path from your dorm to each of the other vertices. (Measure shortness in terms of the number of edges in your graph, not the distance each edge represents.)

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Chapter 6.4, Problem 7MS

Chapter 6.4, Problem 9MS

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Question 1 i Let G be the graph given by the following drawing. g a d b (a) Draw the induced subgraph of G on vertex set {a, d, e, f, g, h}. [4] (b) Draw a subgraph of G that is isomorphic to the graph H with V (H) = {r, s, t, u, v, w, x, y, z} and E(H) = {rs, rt, ru, st, sv, tw, ux, vy, wz}. (c) Draw a spanning tree of G whose set of leaves is {a, b, g, j}, or explain why such a spanning tree does not exist. [4] [4] Call a cycle of a graph H a Hamiltonian cycle of H if it contains every vertex of H. (d) Give a Hamiltonian cycle of G, or explain why such a cycle does not exist. Let G be an arbitrary simple graph, n = = |V(G)|, and m = |E(G)|. [4] (e) Assume that the complement of G is connected. Show that m ≤ ½n² − ³n +1. [8]

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Chapter 6 Solutions

The Heart of Mathematics: An Invitation to Effective Thinking

Ch. 6.1 - Map maker, map maker make me a graph. Represent...Ch. 6.1 - Unabridged list. Represent cach landmass from...Ch. 6.1 - Will the walk work? Does your graph from...Ch. 6.1 - Walk around the house. Is it possibel to traverse...Ch. 6.1 - Walk the line. Does this graph above have an Euler...Ch. 6.1 - Walkabout. Does this graph have an Euler circuit?...Ch. 6.1 - Linking the loops. In this map, the following...Ch. 6.1 - Scenic drive. (S) Here is a map of Rockystone...Ch. 6.1 - Under-edged. (H) Does this graph have an Euler...Ch. 6.1 - No man is an island. The country of Pelago...

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