25. Let G be a connected, undirected graph, and let V be the set of all vertices in G. Define a relation R on V as follows: for any vertices a, b e V, a Rb if there is a path from a to b with an even number of edges. (A path may use the same edge more than once.) Prove that R is an equivalence relation.
25. Let G be a connected, undirected graph, and let V be the set of all vertices in G. Define a relation R on V as follows: for any vertices a, b e V, a Rb if there is a path from a to b with an even number of edges. (A path may use the same edge more than once.) Prove that R 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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Essentials of DISCRETE MATHEMATICS
Section 2.4 - Relations and Equivalences
Transcribed Image Text:25. Let G be a connected, undirected graph, and let V be the set of all vertices
in G. Define a relation R on V as follows: for any vertices a, b e V, a Rb
if there is a path from a to b with an even number of edges. (A path
may use the same edge more than once.) Prove that R is an equivalence
relation.
26. Suppose the equivalence relation of Exercise 25 is defined on the vertices
of the following graph. What are the equivalence classes?
of
a
d.
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