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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access September 25, 2015

A class of zero divisor rings in which every graph is precisely the union of a complete graph and a complete bipartite graph

  • Syed Khalid Nauman EMAIL logo and Basmah H. Shafee
From the journal Open Mathematics

Abstract

Recently, an interest is developed in estimating genus of the zero-divisor graph of a ring. In this note we investigate genera of graphs of a class of zero-divisor rings (a ring in which every element is a zero divisor). We call a ring R to be right absorbing if for a; b in R, ab is not 0, then ab D a. We first show that right absorbing rings are generalized right Klein 4-rings of characteristic two and that these are non-commutative zero-divisor local rings. The zero-divisor graph of such a ring is proved to be precisely the union of a complete graph and a complete bipartite graph. Finally, we have estimated lower and upper bounds of the genus of such a ring.

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Received: 2015-2-22
Accepted: 2015-8-13
Published Online: 2015-9-25

© 2015

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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