A BIPARTITE GRAPH ASSOCIATED TO A BI-MODULE OF A RING

Authors

  • Z. Fattahi Ferdowsi University of Mashhad International Campus
  • A. Erfanian Ferdowsi University of Mashhad - Department of Pure Mathematics and Center of Excellence in Analysis on Algebraic Structures
  • A. Azimi University of Neyshabur - Department of Mathematics

Keywords:

Bi-module, diameter, girth, bipartite, planar, vertex and edge connectivity

Abstract

Let R be a ring, M be a left and right R-module.  We associate a bipartite graph to R-module M of ring R, denoted by ΓR,M as undirected simple graph whose two parts of vertices are R \ CR(M) and M \ CM(R) and two distinct vertices x and y are adjacent if xy ≠  yx, where CR(M) is the set of elements of R that commute with all elements in M.  Some graph theoretical properties of this graph stated in this paper.

Cover of n°40 Italian Journal of Pure and Applied Mathematics

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Published

2018-07-31

How to Cite

Fattahi, Z., Erfanian, A., & Azimi, A. (2018). A BIPARTITE GRAPH ASSOCIATED TO A BI-MODULE OF A RING. Italian Journal of Pure and Applied Mathematics, 40, 157–163. Retrieved from https://journals.uniurb.it/index.php/ijpam/article/view/7042

Issue

N°40 - July 2018

Section

Articoli - Forum Editrice

License

Copyright (c) 2018 Z. Fattahi, A. Erfanian, A. Azimi

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

L'opera è pubblicata sotto  Licenza Creative Commons Attribuzione 4.0 Internazionale (CC-BY)

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