A note on strong zero-divisor graphs of near-rings
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DOI:
https://doi.org/10.26637/MJM0701/0024Abstract
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 $I J=0$. 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 $\operatorname{diam}\left(\Gamma_s(N)\right)>3$, then $N$ is necessarily a strongly semi-prime near-ring. Also we find the $\chi\left(\Gamma_s(N)\right)$ and investigate some characterizations of cliques and maximal cliques in $\Gamma_s(N)$.
Keywords:
Near-ring, essential ideal, diameter, girth, chromatic numberMathematics Subject Classification:
Mathematics- Pages: 122-126
- Date Published: 01-01-2019
- Vol. 7 No. 01 (2019): Malaya Journal of Matematik (MJM)
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