Journal Menu
AN IDEAL-BASED d-ZERO-DIVISOR GRAPH OF COMMUTATIVE RINGS
Pages : [105] - [119]
Received : May 11, 2015
Communicated by : Professor Bao-Xuan Zhu
Abstract
Let I be an ideal of a commutative ring R with an ideal expansion d and for some
In this paper, we introduce and investigate an ideal-based d-zero-divisor graph of R, denoted by
It is the (undirected) graph with vertices
and for distinct
the vertices x and y are adjacent if and only if
An ideal-based zero-divisor graph of a commutative ring, denoted by
is the undirected graph with vertices
for some
and distinct vertices x and y are adjacent if and only if
This is due to Redmond [9]. In the case
the identity function,
Keywords
d-zero-divisor, graph, ideal-based.