Generalized Cayley graphs of rectangular groups
Bull. Korean Math. Soc. 2015 Vol. 52, No. 4, 1169-1183
https://doi.org/10.4134/BKMS.2015.52.4.1169
Published online July 31, 2015
Yongwen Zhu
Yantai University
Abstract : We describe generalized Cayley graphs of rectangular groups, so that we obtain (1) an equivalent condition for two Cayley graphs of a rectangular group to be isomorphic to each other, (2) a necessary and sufficient condition for a generalized Cayley graph of a rectangular group to be (strong) connected, (3) a necessary and sufficient condition for the colour-preserving automorphism group of such a graph to be vertex-transitive, and (4) a sufficient condition for the automorphism group of such a graph to be vertex-transitive.
Keywords : generalized Cayley graph of semigroups, rectangular group, connected graph, isomorphism, colour-preserving automorphism, vertex-transitive
MSC numbers : 05C25, 20B25, 08B15, 20M17
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