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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.

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.

Linear Algebra: A Modern Introduction
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. Do not use ChatGPT and Please type the correct answer to 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.

 

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.
Transcribed Image Text: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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