Answered: 13. Prove that any undirected,…

13. Prove that any undirected, loop-free graph on n vertices with at least (n − 1)(n − 2)/2 + 1edges is connected. Also, give an example of a disconnected n-vertex graph with one fewer edge.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 80EQ

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13. Prove that any undirected, loop-free graph on n vertices with at least (n − 1)(n − 2)/2 + 1
edges is connected. Also, give an example of a disconnected n-vertex graph with one fewer edge.

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