On construction of some new types of semigroups

Abstract

This paper is about the classification of the commuting graphs of semigroups to some extent. Let $S$ be a finite non-commutative semigroup, its commuting graph, denoted by $G(S)$, is a simple graph (which has no loops and multiple edges) whose sets of vertices are elements of $S$ and whose sets of edges are those elements of $S$ which commute with other elements i.e. for any $a,b \in S$ such that $ab=ba$ for $a \neq b$. In this paper, we construct some new types of semigroup of cyclic tree type graphs, sunflower like graphs, almost complete type graphs and almost ladder type graphs with the help of Monid package of GAP.