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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

queries then please email me.

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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