THE ZERO-DIVISOR GRAPHS OF RINGS AND SEMIRINGS-Reference-Cited by-同舟云学术

THE ZERO-DIVISOR GRAPHS OF RINGS AND SEMIRINGS

Published:2012-06 Issue:04 Volume:22 Page:1250033
ISSN:0218-1967
Container-title:International Journal of Algebra and Computation
language:en
Short-container-title:Int. J. Algebra Comput.

Author:

DOLŽAN DAVID¹,OBLAK POLONA²

Affiliation:

1. Department of Mathematics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia

2. Faculty of Computer and Information Science, University of Ljubljana, Tržaška 25, SI-1000 Ljubljana, Slovenia

Abstract

In this paper we study zero-divisor graphs of rings and semirings. We show that all zero-divisor graphs of (possibly noncommutative) semirings are connected and have diameter less than or equal to 3. We characterize all acyclic zero-divisor graphs of semirings and prove that in the case zero-divisor graphs are cyclic, their girths are less than or equal to 4. We find all possible cyclic zero-divisor graphs over commutative semirings having at most one 3-cycle, and characterize all complete k-partite and regular zero-divisor graphs. Moreover, we characterize all additively cancellative commutative semirings and all commutative rings such that their zero-divisor graph has exactly one 3-cycle.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218196712500336

Reference24 articles.

1. On the zero-divisor graph of a commutative ring

2. Zero-divisor graphs of non-commutative rings

3. On zero-divisor graphs of finite rings

4. On the Zero-Divisor Graph of a Ring

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