A GENERALIZED IDEAL BASED-ZERO DIVISOR GRAPHS OF NEAR-RINGS

Title & Authors
A GENERALIZED IDEAL BASED-ZERO DIVISOR GRAPHS OF NEAR-RINGS
Dheena, Patchirajulu; Elavarasan, Balasubramanian;

Abstract
In this paper, we introduce the generalized ideal-based zero-divisor graph structure of near-ring N, denoted by $\small{\widehat{{\Gamma}_I(N)}}$. It is shown that if I is a completely reflexive ideal of N, then every two vertices in $\small{\widehat{{\Gamma}_I(N)}}$ are connected by a path of length at most 3, and if $\small{\widehat{{\Gamma}_I(N)}}$ contains a cycle, then the core K of $\small{\widehat{{\Gamma}_I(N)}}$ is a union of triangles and rectangles. We have shown that if $\small{\widehat{{\Gamma}_I(N)}}$ is a bipartite graph for a completely semiprime ideal I of N, then N has two prime ideals whose intersection is I.
Keywords
ideal-based zero-divisor graph;diameter;near-ring;ideal and cycle;
Language
English
Cited by
1.
On generalized zero divisor graph of a poset, Discrete Applied Mathematics, 2013, 161, 10-11, 1490
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