[GAP Forum] {Spam?} Cayley sum graph

[Stephen Linton]

Dear GAP Forum,

The  immediate problem with the example below is the OnPoints action, which doesn't know how to 
conjugate an element of G by a permutation. You can OnPoints by 

function(x,g) return x; end

since you actually have no action (of the trivial group), which will allow you to construct the graph.

However, there are neither facilities for drawing the graph, nor for checking Hamiltonicity, in GAP, since the GRAPE package which provides out Graph functionality has other purposes, so I'm not sure how far this will get you.

	Yours

		Steve Linton

On 16 Aug 2011, at 08:22, ç wrote:

> 
> 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.
> 
> 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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