Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 10 - Graphs and Trees - Exercise Set 10.1 - Page 640: 9

Answer

(i) e1, e2, and e7 are incident on v1. (ii) v1 and v2 are adjacent to v3. (iii) e2, and e7 are adjacent to e1. (iv) Loops are e1 and e3. (v) e4 and e5 are parallel. (vi) v4 is an isolated vertex. (vii) degree of v3 = 2 (viii) total degree = 14

Work Step by Step

An edge with just one endpoint is called a loop, and two or more distinct edges with the same set of endpoints are said to be parallel. An edge is said to connect its endpoints; two vertices's that are connected by an edge are called adjacent; and a vertex that is an endpoint of a loop is said to be adjacent to itself. An edge is said to be incident on each of it s endpoints, an d two edges incident on the same end point are called adjacent. A vertex on which no edges are incident is called isolated
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