Hi:

I am using the command

Gamma:= CayleyGraph(G)

(from GRAPE) in order to construct the Cayley graph of a certain group. I
was wondering whether there is an obvious action of G on the vertices of
Gamma.

Namely, I would like to take elements of Gamma at distance Diameter(Gamma)
from the identity element (easily done with Layers) and then multiply by
inverses of elements in the generating set and then compute the distance
of the new element from the identity.

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.)

I've looked at the GRAPE documentation and the e-mail on using Cayley
graphs from a couple of months back, but nothing seemed to help. I am
using GAP3R4P4. (Yes, I'm one of them non-UNIX crazies :)

Thanks in advance for all suggestions/help.

-- K.M.

**********************************************************************
* Kaustuv Mukul Das                                                  *
* Department of Mathematics             DON'T PANIC                  *
* Eastern Illinois University                                        *
* Charleston, IL 61920                            --  Douglas Adams  *  
* (217) 581 3828                                                     *
**********************************************************************

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