QUESTION 13. Recall that, in graph, a walk of length n20 from vertex a to b is an alternating sequence of vertices and edges voe11e202e3... Un-1enn, where to = a and Un=b, vi-1 and v; are ends of edge e,, i 1, 2, 3,..., n. Let G be a graph with vertex set V, define a relation R from V to V as follows: Letu, v E V, (u, v) E R if and only if there exists a walk fromu to v. Prove that this relation is an equivalence relation.
QUESTION 13. Recall that, in graph, a walk of length n20 from vertex a to b is an alternating sequence of vertices and edges voe11e202e3... Un-1enn, where to = a and Un=b, vi-1 and v; are ends of edge e,, i 1, 2, 3,..., n. Let G be a graph with vertex set V, define a relation R from V to V as follows: Letu, v E V, (u, v) E R if and only if there exists a walk fromu to v. Prove that this relation is an equivalence relation.
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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Transcribed Image Text:QUESTION 13.
Recall that, in graph, a walk of length n ≥0 from vertex a to b is an alternating sequence of
vertices and edges voe11e202e3... Un-1enn, where to = a and Un=b, vi-1 and v; are ends
of edge e,, i 1, 2, 3,..., n.
Let G be a graph with vertex set V, define a relation R from V to V as follows:
Letu, v E V, (u, v) E R if and only if there exists a walk fromu to v.
Prove that this relation is an equivalence relation.
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