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Graph Theory - connection proof

  • Thread starter oneamp
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  • #1
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Homework Statement



Prove that if a graph has > (n-1)(n-2) /2 edges, it is connected.

Homework Equations



??

The Attempt at a Solution



I've drawn several examples and made tables, and I can see that the graph is indeed connected if it has more edges than [(n-1)(n-2)]/2. But what I cannot do so far is prove it. How can I start doing this proof?

Thanks
 

Answers and Replies

  • #2
33,518
5,196

Homework Statement



Prove that if a graph has > (n-1)(n-2) /2 edges, it is connected.

Homework Equations



??

The Attempt at a Solution



I've drawn several examples and made tables, and I can see that the graph is indeed connected if it has more edges than [(n-1)(n-2)]/2. But what I cannot do so far is prove it. How can I start doing this proof?

Thanks
What does n represent here?
How does your book define "connected" graph?
 
  • #3
219
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n is the number of vertices. Connected graph means that there is no vertex that is not connected to any other by some path. Also the graph is undirected and simple (simple meaning no loops, no more than one edge between any two vertexes.)
 
  • #4
Office_Shredder
Staff Emeritus
Science Advisor
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You might want to do the opposite proof: if a graph is disconnected, it has fewer than or equal to (n-1)(n-2)/2 edges.

In particular it shouldn't be hard to construct the disconnected graph with the most edges.
 
  • #5
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That helped, thank you.
 

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