1. Below is depicted a graph G constructed by joining two opposite vertices of C12. Some authors call this a "theta graph" because it resembles the Greek letter 0. a. What is the total degree of this graph? b. What are the possible total degrees of graphs obtained by deleting a vertex of G? c. What are the possible total degrees of graphs obtained by contracting an edge of G? d. What are the possible total degrees of graphs obtained by identifying two vertices of G?

1. Below is depicted a graph G constructed by joining two opposite vertices of C12. Some authors call this a "theta graph" because it resembles the Greek letter 0. a. What is the total degree of this graph? b. What are the possible total degrees of graphs obtained by deleting a vertex of G? c. What are the possible total degrees of graphs obtained by contracting an edge of G? d. What are the possible total degrees of graphs obtained by identifying two vertices of G?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

1. Below is depicted a graph G constructed by joining two opposite
vertices of C12. Some authors call this a "theta graph" because it
resembles the Greek letter 0.
a. What is the total degree of this graph?
b. What are the possible total degrees of graphs obtained by
deleting a vertex of G?
c. What are the possible total degrees of graphs obtained by
contracting an edge of G?
d. What are the possible total degrees of graphs obtained by
identifying two vertices of G?

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