Graph operations on Cayley graphs of semigroups

Abstract

Lots of large graphs can be constructed from existing smaller graphs by using graph operations, such as the graph products. Many properties of such large graphs are closely related to those of the corresponding smaller ones.In this paper we consider some operations of Cayley graphs on semigroups.

Applications of the Cayley graph of a monoid presentation in characterizations for right type B semigroups

“…Let S be a semigroup and T be a nonempty subset of S. The Cayley graph Cay(S, T ) of S relative to T is defined as the graph with vertex set S and edge set E(Cay(S, T )) consisting of those ordered pair (a, b), where a = b and sa = b for some s ∈ T (see, [5,7,14]). The Cayley graphs of semigroups have been investigated by many authors, and a lot of interesting results have been obtained (see, [8][9][10][11][12][13][16][17][18]). The Cayley graphs of semigroups are closely related to finite state automata and have many valuable applications (see, [5-9, 11-13, 18-20]).…”