On the Diameter, Girth and Coloring of the Strong Zero‑Divisor Graph of Near‑rings

Abstract

. In this paper, we study a directed simple graph Γ 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 ∈ 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 Γ 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 Γ s ( N ).