From BRYAN@wvnvm.wvnet.edu Thu Dec 8 15:21:09 1994 Return-Path: Received: from WVNVM.WVNET.EDU by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA15457; Thu, 8 Dec 94 15:21:09 EST Message-Id: <9412082021.AA15457@life.ai.mit.edu> Received: from WVNVM.WVNET.EDU by WVNVM.WVNET.EDU (IBM VM SMTP V2R2) with BSMTP id 5969; Thu, 08 Dec 94 15:21:12 EST Received: from WVNVM.WVNET.EDU (NJE origin BRYAN@WVNVM) by WVNVM.WVNET.EDU (LMail V1.2a/1.8a) with BSMTP id 5408; Thu, 8 Dec 1994 15:21:12 -0500 X-Acknowledge-To: 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 Morgantown, WV 26505 BRYAN@WVNVM.WVNET.EDU