let n>=2 be a natural numberLet V be the set of people in a party of n people. Use set-builder notation o define E in the undirected graph G=(V,E) where there is an edge between two vertices u and v if the person u and v have met each other.What does the degree of edge in G represent?Prove that there cannot be two vertices u and v in V such that deg(u)=0 and deg(v)=n-1 at the same time.Use part 2 and 3 along with pigeon hole principle to show that in every party of n people, there is always two people who both have met exactly the same number of people.

Answer (1) E = { (u,v) , u, v ∈ V | person u and V have met each other}(2) degree of a vertex u of G…

Answered: pigeon hole principle

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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let n>=2 be a natural number

Let V be the set of people in a party of n people. Use set-builder notation o define E in the undirected graph G=(V,E) where there is an edge between two vertices u and v if the person u and v have met each other.
What does the degree of edge in G represent?
Prove that there cannot be two vertices u and v in V such that deg(u)=0 and deg(v)=n-1 at the same time.
Use part 2 and 3 along with pigeon hole principle to show that in every party of n people, there is always two people who both have met exactly the same number of people.

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