5. Let G = (V, E) be a graph with n > 3 vertices.(a) Define a relation on V by "ry if and only if there is a walk between x and y".Prove that is an equivalence relation on V.(b) Give an example of a graph G with 2 connected components.(c) Suppose that dege(x) + degc(y) > n + 4 for all non-adjacent vertices x, y € V. Showthat G has two Hamilton cycles that have no edge in common.(d) Using Kruskal's Greedy Algorithm, find a minimum weight spanning tree of the edgeweighted graph below.I731YW1100132NU 215

Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Answered: 5. Let G=(V, E) be a graph with n > 3…

5. Let G=(V, E) be a graph with n > 3 vertices. (a) Define a relation on V by "ry if and only if there is a walk between r and y". Prove that is an equivalence relation on V.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

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

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

Chapter1: Line And Angle Relationships

Section1.4: Relationships: Perpendicular Lines

Problem 17E: Does the relation is a brother of have a reflexive property consider one male? A symmetric property...

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Question

5. Let G = (V, E) be a graph with n > 3 vertices.
(a) Define a relation on V by "ry if and only if there is a walk between x and y".
Prove that is an equivalence relation on V.
(b) Give an example of a graph G with 2 connected components.
(c) Suppose that dege(x) + degc(y) > n + 4 for all non-adjacent vertices x, y € V. Show
that G has two Hamilton cycles that have no edge in common.
(d) Using Kruskal's Greedy Algorithm, find a minimum weight spanning tree of the edge
weighted graph below.
I
7
3
1
Y
W
1
100
1
3
2
N
U 2
15

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