Volume no :2, Issue no: 1, September (2009)

Journal of Algebra, Number Theory: Advances and Applications

COMMUTATIVE RINGS AND ZERO-DIVISOR SEMIGROUPS OF SIMPLE
GRAPH

Author's: Gaohua Tang, Huadong Su and Yangjiang Wei
Pages: [1] - [11]
Received Date: July 13, 2009
Submitted by:

Abstract

In this paper, we study commutative rings and commutative zero-divisor semigroups determined by graphs. We prove that for the graph a complete graph deleted an edge has corresponding semigroups and the graph has corresponding rings, if and only if We obtain a formula to calculate the number of non-isomorphic zero-divisor semigroups corresponding to the graph and by using of a computing programme, the values of are listed for

Keywords

zero-divisor graph, zero-divisor semigroup, commutative ring, complete graph deleted an edge.