Dear GAP Forum,

       X-Miles:        GAP Forum article 127 accepted at 31 Jan 98 10:29 +0100
Date:           Sat, 31 Jan 98 10:29:06 +0000
From: Kaustuv M. Das <cfkmd@ux1.cts.eiu.edu>
To: Multiple recipients of list <GAP-Forum@dcs.st-and.ac.uk>
Subject:        Action of G on CayleyGraph(G)

If I do the following (assuming Distance(Gamma,1,44) = Diameter(Gamma) ):

Distance(Gamma, VertexName(Gamma,44)*s1, 1);

where s1 is an involution in the generating set I get the obvious error
message that VertexName(Gamma, 44)*s1 is not a vertex of Gamma. (It is a
vertex name, but that doesn't seem to help.)

Yes, vertex names are in this case disjoint from vertices.
A general solution (would work for whatever (GRAPE) graphs
would be to define

VertexIndex := function(graph, vertexname)
return Position(graph.names, vertexname);
end;

and use (in your case)
Distance(Gamma, VertexIndex(Gamma, VertexName(Gamma,44)*s1), 1);

Hope this helps,

Dmitrii
d.pasechnik@twi.tudelft.nl
http://ssor.twi.tudelft.nl/~dima