lescanne@LORIA.CRIN.FR (Pierre Lescanne) (05/16/91)
Does someone knows a good reference on "Group diagram" also called
"Cayley diagrams" or "Group graphs", especially with reference to
algorithms? My only reference is:
AUTHOR = {W.~Magnus and A.~Karrass and D.~Solitar},
TITLE = {Combinatorial Group Theory},
PUBLISHER = {Interscience},
YEAR = {1966},
VOLUME = {13},
SERIES = {Pure and Applied Mathematics}
Pierre LESCANNE | Tel: (work) (33) 83 59 30 07
CRIN (CNRS) & INRIA-Lorraine | (home) (33) 83 22 76 92
BP 239 | Fax: (33) 83 27 83 19
F54506 VANDOEUVRE-les-NANCY Cedex FRANCE | E-mail: lescanne@loria.crin.frstiller@cs.jhu.edu (Lewis Stiller) (05/16/91)
In article <9105151724.AA00274@poincare.crin.fr> Pierre Lescanne <lescanne%loria.crin.fr@VM1.NoDak.EDU> writes: >Does someone knows a good reference on "Group diagram" also called >"Cayley diagrams" or "Group graphs", especially with reference to >algorithms? Hi. I'm biased because I use them, but I think that algorithmic implications of group graphs and closely related group action graphs will increase with the newer machines, many of whose interconnection networks are group action graphs. For instance, a simple fact that is not universally known is that the hypercube and torus are group graphs so algorithms that use those networks are using group graphs; of course, the group machinery is unnecessary for many algorithms. A. Rosenberg and his group (v.i.) are real experts in this. Anyway, here are just a few of the things you might find interesting: @article{akers:groupgraphs, author="S.B. Akers and B. Krishnamorthy", title="On group graphs and their fault tolerance", journal="IEEE Trans. Comput.", volume="C-36", pages="885-888", year=1987 } @techreport{annexstein:groupactiongraphs, title="Group action graphs and parallel architectures", author="Fred Annexstein and Marc Baum\-slag and {Ar\-nold} L. Ro\-senberg", institution="University of Massachusetts", number="COINS Technical Report 87-133", year="1987" } (I heard they have a new edition. This is a really fun book...) @book{white:1984, address="New York", author= "Arthur T. White", title= "Graphs, groups, and surfaces", publisher = "North-Holland/Elsevier", city="New York", year="1984" } @inproceedings{stiller:supercomputing, author="Lewis Stiller", title="Group graphs and computational symmetry on massively parallel architecture", month="October", year=1990, booktitle= "Supercomputing '90", } @techreport{annexstein88, author="Fred Annexstein and Marc Baumslag", title="Hamiltonian circuits in {Cayley} digraphs", institution="University of Massachusetts Computer and Information Science Department", address="Amherst, MA", number="COINS 88-40" } You might or might not be interested in this article which does not explicitly discuss group graphs: @article{hillis:1990, author="Danny Hillis and Washington {Taylor IV}", title="Expoiting symmetry in high-dimensional finite-difference calculations", journal="Journal of Parallel and Distributed Computing", year=1990, volume=8, number=1, month="January", pages="77-79" } I hope this helps a little. Good luck, lewis stiller@cs.jhu.edu