A note on strong zero-divisor graphs of near-rings
Authors :
Prohelika Das 1 *
Author Address :
1 Department of Mathematics, Cotton University, Guwahati-781001, India.
*Corresponding author.
Abstract :
For a near-ring $N$, the strong zero-divisor graph $Gamma_{s}(N)$ is a graph with vertices $V^{*}(N)$, the set of all non-zero left $N$-subset having non-zero annihilators and two vertices $I$ and $J$ are adjacent if and only if $IJ=0$. In this paper, we study diameter and girth of the graph $Gamma_{s}(N)$ wherein the nilpotent and invariant vertices are playing a significant role. We show that if $diam(Gamma_{s}(N))>3$, then $N$ is necessarily a strongly semi-prime near-ring. Also we find the $chi (Gamma_{s}(N))$ and investigate some characterizations of cliques and maximal cliques in $Gamma_{s}(N)$.
Keywords :
Near-ring; essential ideal; diameter; girth; chromatic number.
DOI :
Article Info :
Received : October 21, 2018; Accepted : January 19, 2019.
