Some properties of Square element graphs over semigroups

Abstract

The Square element graph over a semigroup is a simple undirected graph whose vertex set consists precisely of all the non-zero elements of , and two vertices are adjacent if and only if either or belongs to the set , where 1 is the identity of the semigroup (if it exists). In this paper, we study the various properties of . In particular, we concentrate on square element graphs over three important classes of semigroups. First, we consider the semigroup formed by the ideals of . Afterwards, we consider the symmetric groups and the dihedral groups . For each type of semigroups mentioned, we look into the structural and other graph-theoretic properties of the corresponding square element graphs.

Keywords

• square element graph
• semigroup
• semigroup of ideals
• symmetric group
• dihedral group