On the extended zero-divisor graph of strictly partial transformation semigroup

Abstract

Given a commutative ring $R$, the zero-divisor graph of $R$ is an undirected simple graph with vertices the nonzero zero-divisors of $R$, and two distinct vertices $x$ and $y$ are adjacent if and only if $xy=0$. In [8], Redmond presented different versions of zero-divisor graphs of noncommutative rings. The main aim of this paper is to analyse these graphs for the semigroup $\mathcal{SP}_{n}$ of all strictly partial transformations on the set $X_{n}=\{1,2,\dots,n\}$.