p. 175 - 180 Characterization of simple orbit graphs
A. Bretto, A. Faisant, C. Jaulin and J. Tomanová Received: March 9, 2009;
Revised: February 2, 2010;
Accepted: May 5, 2010
Abstract.
Let G be a (finite) group and let S be a non-empty subset of
G. The vertex set of the orbit graph O(G,S) is the
collection, over all s Î S, of orbits of left translations
induced by s. If u and v are distinct vertices (each
representing an orbit of some s and t from S), then for any
gÎ G appearing in both orbits there is an edge colored g in
O(G,S) joining u and v. Orbit graphs are an important
special case of "G-graphs" introduced by Bretto and Faisant in
Math. Slovaca 55 (2005). In this paper we characterize simple orbit graphs and apply the result to show that certain
class of simple orbit graphs is closed under the
construction of incidence graphs.
Keywords:
orbit graph, G-graph, automorphism group
AMS Subject classification:
Primary: 05C25
PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2010, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |