On Cayley Graphs of Rees Matrix Semigroups Relative to Green’s Equivalence L-Class.

In 1878, Cayley introduced graphs of groups. Later, graphs of semigroups were introduced as generalization of Cayley graphs of groups. In 1940, Rees introduced matrix semigroups. In this paper, we describe some properties of Cayley graphs of Rees matrix semigroups. We see that, for a group G and for any arbitrary non-empty finite sets I and Λ, the Cayley graph of the Rees matrix semigroup S = M(G; I,Λ; P) relative to any Green’s equivalence L-class of S has a Hamiltonian decomposition consisting of |Λ| components.Moreover, when |G| × |I| is odd, we show that the decomposition is Eulerian. [ABSTRACT FROM AUTHOR]