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: 8

Answer

(i) e1, e2, and e3 are incident on v1. (ii) v1, v2, and v3 are adjacent to v3. (iii) e2, e8, e9, and e3 are adjacent to e1. (iv) Loops are e6 and e7. (v) e8 and e9 are parallel; e4 and e5 are parallel. (vi) v6 is an isolated vertex. (vii) degree of v3 = 5 (viii) total degree = 20

Work Step by Step

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