@article {IOPORT.05610940,
    author       = {Khosravi, Bahman},
    title        = {On Cayley graphs of left groups.},
    year         = {2009},
    journal      = {Houston Journal of Mathematics},
    volume       = {35},
    number       = {3},
    issn         = {0362-1588},
    pages        = {745-755},
    publisher    = {University of Houston, Department of Mathematics, Houston, TX},
    abstract     = {From the authors abstract: {\it A. V. Kelarev} and {\it C. E. Praeger} in ["On transitive Cayley graphs of groups and semigroups," Eur. J. Comb. 24, No.1, 59--72 (2003; Zbl 1011.05027)] gave necessary and sufficient conditions for Cayley graphs of semigroups to be vertex-transitive. Also {\it S. Fan} and {\it Y. Zeng}, in ["On Cayley graphs of Bands," Semigroup Forum 74, No. 1, 99--105 (2007; Zbl 1125.05051)] gave a description of all vertex-transitive Cayley graphs of finite bands. In this paper we give similar descriptions for all vertex-transitive Cayley graphs of left groups. Also we extend some of the results to every direct product of a group and a band. Two of the main results are: The direct product $T=B\times B$ of a group $G$ with a left zero band $B$, with $C\subseteq T$ has an $Aut_C(T)$-vertex transitive Cayley graph iff $CT=T$ and $Cay(<C>,C)$ is $Aut_C(T)$-vertex transitive. Let $S$ be asemigroup, $C\subseteq S$ such that all principal left ideals of $<C>$ are finite. If $Cay(S,C)$ is $ColAurt_C(s)$-vertex-transitive, then $Cay(S,C)$ is isomorphic to the Cayley graph of a group.},
    reviewer     = {Ulrich Knauer (Oldenburg)},
    identifier   = {05610940},
}