On Comaximal Graphs of Near-rings

- Journal title : Kyungpook mathematical journal
- Volume 49, Issue 2, 2009, pp.283-288
- Publisher : Department of Mathematics, Kyungpook National University
- DOI : 10.5666/KMJ.2009.49.2.283

Title & Authors

On Comaximal Graphs of Near-rings

Dheena, Patchirajulu; Elavarasan, Balasubramanian;

Dheena, Patchirajulu; Elavarasan, Balasubramanian;

Abstract

Let N be a zero-symmetric near-ring with identity and let be a graph with vertices as elements of N, where two different vertices a and b are adjacent if and only if + ** = N, where ** is the ideal of N generated by x. Let be the subgraph of generated by the set {n N : = N} and be the subgraph of generated by the set , where is the set of all vertices of a graph G. In this paper, we completely characterize the diameter of the subgraph of . In addition, it is shown that for any near-ring, is a complete bipartite graph if and only if the number of maximal ideals of N is 2, where M(N) is the intersection of all maximal ideals of N and is the graph obtained by removing the elements of the set M(N) from the vertices set of the graph .

Keywords

ideal;diameter;complete and complete bipartite graph;

Language

English

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