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Date: Thu, 8 Dec 1994 15:21:04 -0500 (EST)
From: "Jerry Bryan"
To:
Subject: Re: Cayley Graphs
In-Reply-To: Message of 12/07/94 at 20:46:00 from ,
Martin.Schoenert@math.rwth-aachen.de
On 12/07/94 at 20:46:00 Martin Schoenert said:
>The Cayley graph Gamma for a group G generated by a certain system of
>generators < g_1, g_2, ... > is defined as follows.
>The vertices of Gamma correspond to the elements of G. From vertex v_1
>draw an edge to v_2 labelled with g_i, if and only if v_1 g_i = v_2.
>Also draw an edge from v_2 to v_2 labelled g_i^-1 (or g_i').
v_1
>So the Cayley graph depends on the group *and* on the generating system.
>Simple, isn't it.
These are fine points, but they bother me anyway.
1. Suppose I write =. If I mean that the group is equal
to the group , then the equation is correct. If I mean that
the Cayley graph of is the same as the Cayley graph of ,
then the equation is incorrect. Which is the conventional meaning?
Is the meaning universal, or does it depend on the author and the
context?
2. I gather from your note and from things that Dan sent me that
one should not list inverses of the generators. For example,
__ is sufficient and one should not write ____. But
people conventionally write __ which includes six processes and
their six inverses. Is this acceptable usage, or should we write
__ instead?
As an additional comment, I have frequently written about the Q length
of a process in ____ or the Q+H length of a process in ____. I think
we would be better served to talk about the length of a process in
____ or the length of a process in ____ if the generator
notation implies a particular Cayley graph.
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
Robert G. Bryan (Jerry Bryan) (304) 293-5192
Associate Director, WVNET (304) 293-5540 fax
837 Chestnut Ridge Road BRYAN@WVNVM
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__