Balanced zero-divisor graphs of matrix rings.

Lobachevskii Journal of Mathematics Vol. 34, Nº 2, pp. 137 - 141, April, 2013.

ISSN (print): 1995-0802
ISSN (online): 1818-9962

Scimago Journal Ranking: 0,27 (in 2013)

Digital Object Identifier:

United Nations Strategic Development Goal - Industry, Innovation and Infrastructure

Abstract

LetR be a finite commutative ringwith identity.We prove that ifR is a principal ideal ring
then the directed zero-divisor graph Ã(Mn(R)) is balanced and eulerian. We also find the smallest
finite commutative ring R with identity such that Ã(Mn(R)) is not balanced.

Basic Sciences and Enabling Technologies

Balanced zero-divisor graphs of matrix rings.