Generalized Cayley graphs of semigroups II

摘要

Following Zhu (Semigroup Forum, 2011, doi:10. 1007/s00233-011-9368-9), we study generalized Cayley graphs of semigroups. The Cayley D-saturated property, a particular combinatorial property, of generalized Cayley graphs of semigroups is considered and most of the results in Kelarev and Quinn (Semigroup Forum 66:89-96, 2003), Yang and Gao (Semigroup Forum 80:174-180, 2010) are extended. In addition, for some basic graphs and their complete fission graphs, we describe all semigroups whose universal Cayley graphs are isomorphic to these graphs.