August 1st, 2010, 04:33 PM  #1 
Member Joined: Feb 2009 Posts: 76 Thanks: 0  Graph theory
Let G be a graph (or multigraph). Determine the number of edges in V for the following situations. a) G is regular (that is each vertex has the same degree) with 15 edges. Determine all the possibilities. hmmm...I was able to construct a graph for this. However, the question asks for 'all the possibilities'. Is there a theorem or formula (or trick) to determine it without having to draw them out U_U. I've seen formulas and theorems in the book but they are about finding the number of edges/vertices or whether the graph is a euler circuit/path by the number of degrees. I can't seem to find one that helps you determine the number of possibilities or how many number of path ways to get from a vertex to another vertex. It seems that I have to do this manually... Id thought Id ask just in case there is one. Thanks in advance 
August 1st, 2010, 07:12 PM  #2 
Member Joined: Feb 2009 Posts: 76 Thanks: 0  Re: Graph theory
Hmm i think I found one that may be useful... It's called the Dijkstra's algorithm. 

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