Explanation Given Information: Suppose G is a graph with n vertices, n edges, and no vertices of degree 0 or 1. Proof: A proposition states that for a graph the sum of the degree of vertices equals twice the number of edges. ∑ v ∈ V deg v = 2 | ε | …….(1) As the degree of a vertex is not 0 or 1, it must be at least 2. The degree of vertex is at least 2, so: ∑ v ∈ V deg v = 2 n + k , k > 0 ……

Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)

3rd Edition

ISBN: 9780134689555

Author: Edgar Goodaire, Michael Parmenter

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 9, Problem 12RE

To determine

Every vertex of G has degree 2.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9, Problem 11RE

Chapter 9, Problem 13RE

Students have asked these similar questions

The 173 acellus.com StudentFunctions inter ooks 24-25/08 R Mastery Connect ac ?ClassiD-952638111# Introduction - Surface Area of Composite Figures 3 cm 3 cm 8 cm 8 cm Find the surface area of the composite figure. 2 SA = [?] cm² 7 cm REMEMBER! Exclude areas where complex shapes touch. 7 cm 12 cm 10 cm might ©2003-2025 International Academy of Science. All Rights Reserved. Enter

2 x²+1 dx x47x²+1

Question attached

Chapter 9 Solutions

Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)

Ch. 9.1 - (Answers can be found in the back of the book.) 1....Ch. 9.1 - (Answers can be found in the back of the book.) 2....Ch. 9.1 - (Answers can be found in the back of the book.)...Ch. 9.1 - (Answers can be found in the back of the book.)...Ch. 9.1 - (Answers can be found in the back of the book.) 5....Ch. 9.1 - Prob. 6TFQ Ch. 9.1 - Prob. 7TFQ Ch. 9.1 - Prob. 8TFQ Ch. 9.1 - Prob. 9TFQ Ch. 9.1 - Prob. 10TFQ

Ch. 9.1 - 1. [BB](Fictitious) A recently discovered map of...Ch. 9.1 - Prob. 2E Ch. 9.1 - 3. One of the owners of the houses in the Three...Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - You and a friend meet three other couples at a...Ch. 9.1 - 8. (a) A graph has six vertices, every two of...Ch. 9.1 - [BB] A graph has six vertices, every two of which...Ch. 9.1 - Prob. 10E Ch. 9.1 - Prob. 11E Ch. 9.2 - Prob. 1TFQ Ch. 9.2 - Prob. 2TFQ Ch. 9.2 - Prob. 3TFQ Ch. 9.2 - (Answers can be found in the back of the book.) is...Ch. 9.2 - Prob. 5TFQ Ch. 9.2 - Prob. 6TFQ Ch. 9.2 - Prob. 7TFQ Ch. 9.2 - Prob. 8TFQ Ch. 9.2 - Prob. 9TFQ Ch. 9.2 - Prob. 10TFQ Ch. 9.2 - Prob. 1E Ch. 9.2 - Prob. 2E Ch. 9.2 - Prob. 3E Ch. 9.2 - Prob. 4E Ch. 9.2 - Prob. 5E Ch. 9.2 - Prob. 6E Ch. 9.2 - Prob. 7E Ch. 9.2 - Draw a graph with 64 vertices representing the...Ch. 9.2 - Consider again the graph accompanying Exercise 5...Ch. 9.2 - Prob. 10E Ch. 9.2 - Prob. 11E Ch. 9.2 - Prob. 12E Ch. 9.2 - 13. [BB] At most social functions, there is a lot...Ch. 9.2 - Prob. 14E Ch. 9.2 - 15. [BB;(a)] for each pair of graphs shown,...Ch. 9.2 - Prob. 16E Ch. 9.2 - Prob. 17E Ch. 9.2 - For each of the following sequences, determine if...Ch. 9.2 - Prob. 19E Ch. 9.2 - [BB] A graph has five vertices of degree 4 and two...Ch. 9.2 - Determine whether each of the graphs in Fig 9.23...Ch. 9.2 - Prob. 22E Ch. 9.2 - Prob. 23E Ch. 9.2 - 24. [BB](requires calculus) Prove that the number...Ch. 9.2 - Prob. 25E Ch. 9.2 - Prob. 26E Ch. 9.2 - Prob. 27E Ch. 9.2 - Prob. 28E Ch. 9.2 - Prob. 29E Ch. 9.2 - Prob. 30E Ch. 9.2 - Prob. 31E Ch. 9.2 - Prob. 32E Ch. 9.2 - Prob. 33E Ch. 9.2 - Prob. 34E Ch. 9.2 - Prob. 35E Ch. 9.3 - (Answers can be found in the back of the book.) It...Ch. 9.3 - Prob. 2TFQ Ch. 9.3 - Prob. 3TFQ Ch. 9.3 - Prob. 4TFQ Ch. 9.3 - Prob. 5TFQ Ch. 9.3 - (Answers can be found in the back of the book.) 6....Ch. 9.3 - (Answers can be found in the back of the book.) If...Ch. 9.3 - Prob. 8TFQ Ch. 9.3 - Prob. 9TFQ Ch. 9.3 - Prob. 10TFQ Ch. 9.3 - [BB] For each of the ten pairs of graphs that can...Ch. 9.3 - Prob. 2E Ch. 9.3 - [BB] Draw all nonisomorphic graphs on n =3...Ch. 9.3 - [BB;(b)] for each pair of grpahs shown. If the...Ch. 9.3 - Prob. 5E Ch. 9.3 - Prob. 6E Ch. 9.3 - Prob. 7E Ch. 9.3 - [BB] Prove that two graphs that are isomorphic...Ch. 9.3 - Consider the following three graphs. [BB] How many...Ch. 9.3 - Prob. 10E Ch. 9.3 - Prob. 11E Ch. 9 - 1. In the Konigsberg Bridge Problem, a tragic fire...Ch. 9 - 2. (a) Draw a configuration of four houses and two...Ch. 9 - 3. Find the solutions, where possible, for the...Ch. 9 - Draw a graph with six vertices at least three of...Ch. 9 - For each of the following sequences, determine if...Ch. 9 - 6. (a) Does there exist a graph with degree...Ch. 9 - Determine whether or not each of the following...Ch. 9 - Answer these questions for each sequence: Does...Ch. 9 - Find a necessary and sufficient condition for the...Ch. 9 - Prob. 10RE Ch. 9 - Suppose a graph has 49 vertices, each of degree 4...Ch. 9 - Prob. 12RE Ch. 9 - A graph G has 50 edges, four vertices of degree 2,...Ch. 9 - Prob. 14RE Ch. 9 - For each pair of graphs shown in fig 9.30 If the...Ch. 9 - Prob. 16RE Ch. 9 - 17. For each of the following cases, explain why...Ch. 9 - George is examining three graphs G1, G2, G3. He...Ch. 9 - Answer Exercise 18 again, assuming that Georges...Ch. 9 - Prob. 20RE

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.

Every vertex of G has degree 2.

Solution Summary: The author explains that every vertex of mathcalG has degree 2. The sum of the degrees of vertices equals twice the number of edges.

Videos

Every vertex of G has degree 2.

Want to see the full answer?

Chapter 9 Solutions