13. In the graph below, determine whether the following walks are trails, paths,closed walks, circuits, simple circuits, or just walks.b. V2V3V4V5 V2d. UUυς Ό) Ό; U4 U)f. v5v4V2V1a. vjezvzezv3e4V4e5V2e2V1e¡voc. V4V2V3V4V5 Vv2 V4e. VOV5V2V3V4V2V|V3eze2v2e4voese9e7esej0e 6V4v5

Walk: A walk is a sequence of vertices and edges of a graph. Trail: Trail is an open walk in which no edge is repeated but vertex can be repeated. Path: It is a trail in which neither vertices nor edges are repeated. Closed walk: A walk is said to be a closed walk if the starting and ending vertices are same. Circuit: Traversing a graph such that not an edge is repeated but vertex can be repeated and it is closed also. Simple circuit: A simple circuit is a closed walk that does not contain any repeated edges or repeated vertices except of course the first and lasta) v1e2v2e3v3e4v4e5v2e2v1e1v0 In this walk vertex v1 and edge e2 are repeated, hence it is just walk. b) v2v3v4v5v2 In this walk starting and ending vertex is same hence it is closed walk. Also none of the edge and vertex are repeated hence it is simple circuit. c) v4v2v3v4v5v2v4 In this walk both edge e5 and vertices v4, v2 are repeated hence it is just walk. d) v2v1v5v2v3v4v2 In this walk only vertex v2 is repeated and it is closed hence it is circuit. e) v0v5v2v3v4v2v1 In this walk only vertex v2 is repeated and it is not closed hence it is trail. f) v5v4v2v1 In this walk neither edges nor vertices are repeated hence it is path. Answer: a) Just walk b) Simple circuit c) Just walk d) Circuit e) Trail f) Path

Math

Advanced Math

13. In the graph below, determine whether the following walks are trails, paths, closed walks, circuits, simple circuits, or just walks. b. V2V3V4V5V2 d. vzv1 V5V2V3 V4 V2 f. v5v4v2V1 a. vjezvzezvze4V4@5Vze2VjejV0 c. V¼V2V3V4V5 V2 V4 e. VOV5V2V3V4V2 V I V3 ez v2 e5 e2 e4 e7 e10 e 6 VA v5

13. In the graph below, determine whether the following walks are trails, paths, closed walks, circuits, simple circuits, or just walks. b. V2V3V4V5V2 d. vzv1 V5V2V3 V4 V2 f. v5v4v2V1 a. vjezvzezvze4V4@5Vze2VjejV0 c. V¼V2V3V4V5 V2 V4 e. VOV5V2V3V4V2 V I V3 ez v2 e5 e2 e4 e7 e10 e 6 VA v5

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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