Proof: inequality involving vertices and edges of a graph

restin84 · April 3rd, 2012, 02:20 PM

I have a proof to do for school.

Prove that in any simple graph G with n vertices and m edges, 2m <= n^2 - n

I just need a little push in the right direction. I'm having trouble even coming up with a starting point. I also cannot find many problems similar to this one so that I may practice.

A little advice would be appreciated

octahedron · April 3rd, 2012, 02:47 PM

Little advice: when number of edges in graph is maximal each vertex is connected with n-1 vertices

restin84 · April 3rd, 2012, 06:10 PM

Quote:

Originally Posted by octahedron

Little advice: when number of edges in graph is maximal each vertex is connected with n-1 vertices

But I could not really say that the number of edges in this particular graph is maximal could I? Do I need cases? Or is the fact that "the number of edges is maximal" in the inequality somehow?

octahedron · April 4th, 2012, 11:10 AM

If the inequality holds for maximal possible number of edges, it holds for every number.

restin84 · April 4th, 2012, 12:12 PM

Okay thanks

April 3rd, 2012, 02:20 PM	#1
restin84 Member Joined: Sep 2009 Posts: 71 Thanks: 0	Proof: inequality involving vertices and edges of a graph I have a proof to do for school. Prove that in any simple graph G with n vertices and m edges, 2m <= n^2 - n I just need a little push in the right direction. I'm having trouble even coming up with a starting point. I also cannot find many problems similar to this one so that I may practice. A little advice would be appreciated
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April 3rd, 2012, 02:47 PM	#2
octahedron Senior Member Joined: Jul 2011 Posts: 118 Thanks: 0	Re: Proof: inequality involving vertices and edges of a grap Little advice: when number of edges in graph is maximal each vertex is connected with n-1 vertices
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April 4th, 2012, 11:10 AM	#4
octahedron Senior Member Joined: Jul 2011 Posts: 118 Thanks: 0	Re: Proof: inequality involving vertices and edges of a grap If the inequality holds for maximal possible number of edges, it holds for every number.
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April 4th, 2012, 12:12 PM	#5
restin84 Member Joined: Sep 2009 Posts: 71 Thanks: 0	Re: Proof: inequality involving vertices and edges of a grap Okay thanks
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