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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.

Operations Research : Applications and Algorithms
Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter2: Basic Linear Algebra
Section2.5: The Inverse Of A Matrix
Problem 10P
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13. Do not use ChatGPT and Please type 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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