Exercise 1 only ExerciseTrue or False? Justify your answer.Let G be a graph.1.If G has no isolated vertex then G is connected.2. If G has a path passing through all of its vertices then(G) ≥ 2.3. If G has a cycle passing through all of its vertices then(G) ≥ 2.4. If a(G) = 1 and G has more than one vertex then G is a complete graph.Exercise 2.Let G be a graph and let a and b E G such that d(a) = A(G) and d(b) = S(G) 2 1. Supposethat b is the unique vertex in G such that d(b) = S(G). Define the following two sets:A = {ve G: d(v) < d(u) Vue N(v)}B = {ve G: d(v) > d(u) u € N(v)}(1) Show that a A.(2) Show that A is a stable set.(3) Suppose that G is a bipartite graph such that G = G(A, B). Show that G containsan even cycle.발W70°F

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Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.5: Rational Functions

Problem 66E

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