Duplicates - which one is wrong?

[Gordon Royle]

On 02/08/2005, at 3:47 AM, Ray Chandler wrote:


> It's not clear to me what differentiates the "multigraph" sequences  
> A000421/A005965 from the "graph" sequences A005638/A002851.
>


"Graph" means "simple graph" in that any two vertices can be joined  
by at most one edge, while "multigraph" means "unrestricted graph" in  
that there can be any number of edges between two vertices - of  
course each of these edges contributes one to the valency (aka  
degree) of its endvertices and so for trivalent (aka cubic) graphs  
there can only be 1, 2 or 3 edges between any two vertices.

Quick example: there is one cubic multigraph on 2 vertices, namely  
two vertices joined by 3 edges, while there are no cubic graphs on 2  
vertices.

All are silently assumed to be loopless, which is an assumption often  
made by graph theorists, but probably should be stated formally in  
the definition of these sequences...


Cheers

gordon
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