Consider the following graph. • V(G) = {v1, v2, v3, v4}, e(G) = {e1, e2, e3, e4, e5}, E(G) = {(e1, [v1, v2]), (e2, [v1, v2]), (e3, [v2, v3]), (e4, [v3, v4]), (e5, [v3, v4])} Draw a picture of the graph on scratch paper to help you answer the following three questions. 1. What is the degree of the graph G? 2. How many simple circuits can be identified in graph G? 2 3. How many walks of length 2 are there from v2 to v4? 2

Consider the following graph. • V(G) = {v1, v2, v3, v4}, e(G) = {e1, e2, e3, e4, e5}, E(G) = {(e1, [v1, v2]), (e2, [v1, v2]), (e3, [v2, v3]), (e4, [v3, v4]), (e5, [v3, v4])} Draw a picture of the graph on scratch paper to help you answer the following three questions. 1. What is the degree of the graph G? 2. How many simple circuits can be identified in graph G? 2 3. How many walks of length 2 are there from v2 to v4? 2

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

Consider the following graph.
●
• V(G) = {v1, v2, v3, v4},
e(G) = {e1, e2, e3, e4, e5},
E(G) = {(e1, [v1, v2]), (e2, [v1, v2]), (e3, [v2, v3]), (e4, [v3, v4]), (e5, [v3, v4])}
Draw a picture of the graph on scratch paper to help you answer the following three questions.
1. What is the degree of the graph G?
2. How many simple circuits can be identified in graph G? 2
3. How many walks of length 2 are there from v2 to v4? 2
Hint: For Q3, use the graph's adjacency matrix and Theorem 10.2.2 on page 709 of the textbook.

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