If G = (V, E) has n > 2 vertices and no self-loops, show that there exist two vertices v # wsuch that deg(v) = deg(w). Present a counterexample, if G is allowed to have self-loops.

Answered: G = (V, E) has n > 2 vertices and no…

G = (V, E) has n > 2 vertices and no self-loops, show that there exist two vertices v w ch that deg(v) = deg(w). Present a counterexample, if G is allowed to have self-loops.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.3: Systems Of Inequalities

Problem 15E

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Question

If G = (V, E) has n > 2 vertices and no self-loops, show that there exist two vertices v # w
such that deg(v) = deg(w). Present a counterexample, if G is allowed to have self-loops.

Expert Solution

Step 1

Graph without self loop is called simple

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