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

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DOI QR Code

Dheena, Patchirajulu;Elavarasan, Balasubramanian

  • 발행 : 2009.04.30

초록

In this paper, we introduce the generalized ideal-based zero-divisor graph structure of near-ring N, denoted by $\widehat{{\Gamma}_I(N)}$. It is shown that if I is a completely reflexive ideal of N, then every two vertices in $\widehat{{\Gamma}_I(N)}$ are connected by a path of length at most 3, and if $\widehat{{\Gamma}_I(N)}$ contains a cycle, then the core K of $\widehat{{\Gamma}_I(N)}$ is a union of triangles and rectangles. We have shown that if $\widehat{{\Gamma}_I(N)}$ is a bipartite graph for a completely semiprime ideal I of N, then N has two prime ideals whose intersection is I.

키워드

ideal-based zero-divisor graph;diameter;near-ring;ideal and cycle

참고문헌

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피인용 문헌

  1. 1. On generalized zero divisor graph of a poset vol.161, pp.10-11, 2013, doi:10.4134/CKMS.2009.24.2.161