graph theory part 3 and 4 Exercise 2.Let G be a graph and let a and be G such that d(a) = A(G) and d(b) = 8(G) > 1. Supposethat b is the unique vertex in G such that d(b) = 5(G). Define the following two sets:A = {vG: 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.****(4) Suppose that A = {u₁, U₂, ..., u.} and B = {V₁, V₁, -, v,} such that u¡v; € E(G) V1 ≤ i ≤s. Show that AUB‡V(G).Exercice 3.

In a graph G, d(v) denotes the degree of a vertex v, which is the number of edges incident to v.Δ(G)…

Answered: (3) Suppose that G is a bipartite graph…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.CT: Test

Problem 6CT: Using the table from Exercise 5, sketch the graph of 2x+3y=12.

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(3) Suppose that G is a bipartite graph such that G = G(A, B). Show that G contains an even cycle. (4) Suppose that A = {u₁, U₂, u,} and B = {v₁, ₁,,,} such that u,v, E E(G)Vi s. Show that AUB V(G).