Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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On the Diameter, Girth and Coloring of the Strong Zero-Divisor Graph of Near-rings

  • Das, Prohelika (Department of Mathematics, Cotton College State University)
  • Received : 2014.05.08
  • Accepted : 2015.01.13
  • Published : 2016.12.23
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Abstract

In this paper, we study a directed simple graph ${\Gamma}_S(N)$ for a near-ring N, where the set $V^*(N)$ of vertices is the set of all left N-subsets of N with nonzero left annihilators and for any two distinct vertices $I,J{\in}V^*(N)$, I is adjacent to J if and only if IJ = 0. Here, we deal with the diameter, girth and coloring of the graph ${\Gamma}_S(N)$. Moreover, we prove a sufficient condition for occurrence of a regular element of the near-ring N in the left annihilator of some vertex in the strong zero-divisor graph ${\Gamma}_S(N)$.

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References

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Cited by

  1. On zero-divisors of near-rings of polynomials pp.1727-933X, 2019, https://doi.org/10.2989/16073606.2018.1455070