[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5666/KMJ.2019.59.4.591

The Zero-divisor Graph of the Ring of Integers Modulo n

Pi, Seung Jun (Department of Mathematics, College of Natural Sciences, Kyungpook National University)
Kim, Se Hun (Department of Mathematics, Seoul National University)
Lim, Jung Wook (Department of Mathematics, College of Natural Sciences, Kyungpook National University)

Publication Information

Kyungpook Mathematical Journal / v.59, no.4, 2019 , pp. 591-601 More about this Journal

Abstract

Let ℤ_n be the ring of integers modulo n and Γ(ℤ_n) the zero-divisor graph of ℤ_n. In this paper, we study some properties of Γ(ℤ_n). More precisely, we completely characterize the diameter and the girth of Γ(ℤ_n). We also calculate the chromatic number of Γ(ℤ_n).

Keywords

zero-divisor graph; ring of integers modulo n; diameter; girth; clique; chromatic number;

Citations & Related Records

Reference

1	D. F. Anderson, M. C. Axtell, and J. A. Stickles, Jr, Zero-divisor graphs in commutative rings, Commutative Algebra: Noetherian and Non-Noetherian Perspectives, 23-45, Springer, New York, 2011.
2	D. F. Anderson and P. S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra, 217(1999), 434-447. DOI
3	D. D. Anderson and M. Naseer, Beck's coloring of a commutative ring, J. Algebra, 159(1993), 500-514. DOI
4	I. Beck, Coloring of commutative rings, J. Algebra, 116(1988), 208-226. DOI
5	S. Mulay, Cycles and symmetries of zero-divisors, Comm. Algebra, 30(2002), 3533-3558. DOI