Dear Mr Ho and Gap-forum,
I am an undergraduate in NUS(National University of Singapore)
doing some research using GAP.
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.
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
queries then please email me.
Regards, Leonard Soicher.
CayleyGraph := function(arg)
# Given a group G=arg and a list gens=arg of
# generators for G, this function constructs a Cayley graph
# for G w.r.t. the generators gens. The generating list
# arg is optional, and if omitted, then we take gens:=G.generators.
# The boolean argument arg 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=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=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.