> < ^ Date: Fri, 16 May 1997 10:43:10 +0100
> < ^ From: Leonard Soicher <l.h.soicher@qmul.ac.uk >
^ Subject: Re: Query on GRAPE

Dear Mr Ho and Gap-forum,

Dear Sir,

I am an undergraduate in NUS(National University of Singapore)
doing some research using GAP.

Question:
1) In Grape, is there specific function to create Cayley Graphs?

Hope you can advise me on the way to generate a cayley graph if
there is no such function in the software.

Thanks,
ShenShyang Ho

There is a CayleyGraph function in GRAPE 2.31 (but it is only documented
in the code). I append this documentation here. If you have any further

Regards, Leonard Soicher.

CayleyGraph := function(arg)
#
# Given a group G=arg[1] and a list gens=arg[2] of
# generators for G, this function constructs a Cayley graph
# for G w.r.t. the generators gens. The generating list
# arg[2] is optional, and if omitted, then we take gens:=G.generators.
# The boolean argument arg[3] is also optional, and if true (the default)
# then the returned graph is undirected (as if gens was closed
# under inversion whether or not it is).
#
# The Cayley graph caygraph which is returned is defined as follows:
# the vertices (actually the vertex names) of caygraph are the elements
# of G; if arg[3]=true (the default) then vertices x,y are
# joined by an edge iff there is a g in gens with y=g*x
# or y=g^-1*x; if arg[3]=false then vertices x,y are
# joined by an edge iff there is a g in gens with y=g*x.
#
# *Note* It is not checked whether G = <gens>. However, even if G
# is not generated by gens, the function still works as described
# above (as long as gens is contained in G), but returns a
# "Cayley graph" which is not connected.
#

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