You are given a graph on n which contains just two disjoint cycles on n/2 vertices (assume that n is even). You select uniformly at random two vertices u and v from G amoung all pair of vertices that do not have an edge between them. Let G 0 ← G ∪ (u, v). That is we insert an edge between u and v. What is the probability that G 0 is connected

You are given a graph on n which contains just two disjoint cycles on n/2 vertices (assume that n is even). You select uniformly at random two vertices u and v from G amoung all pair of vertices that do not have an edge between them. Let G 0 ← G ∪ (u, v). That is we insert an edge between u and v. What is the probability that G 0 is connected

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 74EQ

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Question

You are given a graph on n which contains just two disjoint cycles on n/2 vertices (assume
that n is even). You select uniformly at random two vertices u and v from G amoung all pair of
vertices that do not have an edge between them.
Let G
0 ← G ∪ (u, v). That is we insert an edge between u and v. What is the probability that G
0
is
connected

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