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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 <Q>=<Q,H>. If I mean that the group <Q> is equal

to the group <Q,H>, then the equation is correct. If I mean that

the Cayley graph of <Q> is the same as the Cayley graph of <Q,H>,

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,

<U,R> is sufficient and one should not write <U,U',R,R'>. But

people conventionally write <Q> which includes six processes and

their six inverses. Is this acceptable usage, or should we write

<U,D,L,R,F,B> instead?

As an additional comment, I have frequently written about the Q length

of a process in <U,R> or the Q+H length of a process in <U,R>. I think

we would be better served to talk about the length of a process in

<U,R> or the length of a process in <U,U2,R,R2> 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 Morgantown, WV 26505 BRYAN@WVNVM.WVNET.EDU