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May 1st, 2009, 07:41 AM  #1 
Newbie Joined: May 2009 Posts: 2 Thanks: 0  quantity of edges if graph kregular?
hi all, how much edges does a graph (V=n) max. have, if all nodes have degree k ? (kregular) 
May 1st, 2009, 08:32 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: quantity of edges if graph kregular?
Each vertex has k edges. If you count the edges for each vertex, every edge will be counted twice.

May 2nd, 2009, 01:24 AM  #3 
Newbie Joined: May 2009 Posts: 2 Thanks: 0  Re: quantity of edges if graph kregular?
(k*n)/2 ??? there is sometimes one edge missed 
May 2nd, 2009, 01:13 PM  #4  
Senior Member Joined: Oct 2007 From: Chicago Posts: 1,701 Thanks: 3  Re: quantity of edges if graph kregular? Quote:
In any graph, the following holds: . Where d(v) is the degree of each vertex. Try proving that. It's a straightforward counting argument.  

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