2 (a) Let G be a simple graph with n vertices and m edges where m ≥ (^₂¹) +2. (i) Let u and w be any two non-adjacent vertices. Explain why the graph G\{v, w} has at most (22) edges (where (3) : is the binomial coefficient). a! := (a-b)!!b! (ii) Is G is necessarily Hamiltonian? Justify your answer.
2 (a) Let G be a simple graph with n vertices and m edges where m ≥ (^₂¹) +2. (i) Let u and w be any two non-adjacent vertices. Explain why the graph G\{v, w} has at most (22) edges (where (3) : is the binomial coefficient). a! := (a-b)!!b! (ii) Is G is necessarily Hamiltonian? Justify your answer.
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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