[GAP Forum] Cayley sum graph

[Asst. Prof. Dmitrii (Dima) Pasechnik]

Dear all,

2011/8/16 饶广 <generalrao at hotmail.com>:
>
> Dear forum,
>
> I am new in GAP. Maybe this is just a very simple question.
>
> Cayley sum graph Cay^+(G,S) is a graph on an abelian group G and two vertices are adjacent iff their sum lies in S.
>
> I am trying to draw Cay^+(Z_2\timesZ_6,{(0,1),(1,2),(1,3)}) and do the following in GAP:
>
>>G:=AbelianGroup([2,6]);
>>gen:=GeneratorsOfGroup(G);
>>S:=[gen[2],gen[1]*gen[2]^2,gen[1],gen[1]*gen[2]^3];
>>Graph(Group(()),Elements(G),OnPoints, function(x,y) return x*y in S; end, true);
>
> This returns an error. I guess the problem is how to refer the elements of a group to the vertex set.

you need to do
Graph(G,Elements(G),OnPoints, function(x,y) return x*y in S; end, true);

(assuming you did LoadPackage("grape");)

HTH,
Dmitrii

>
> In addition, I also want to test if this graph is hamiltonian or not. But I couldn't find a direct function for this. Does anyone know about this?
>
>
> Thanks very much,
> Grant
>
>
>
>
>
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Dmitrii Pasechnik
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