Classification of Zero Divisor Graphs of a Commutative Ring With Degree Equal 7 and 8

Abstract

In 2005 J. T Wang investigated the zero divisor graphs of degrees 5 and 6. In this paper, we consider the zero divisor graphs of a commutative rings of degrees 7 and 8.

Classification of Zero Divisor Graphs of Commutative Rings of Degrees 11,12 and 13

“…In [6], Wang investigated the zero divisor graphs of degree 5, 6, 9 and 10. In [5], we consider the zero divisor graphs of degree 7 and 8. In this paper, we extend these results to consider the zero divisor graphs of commutative rings of degrees 11,12 and 13.…”

Idempotent Divisor Graph of Commutative Ring

“…Later in [2], Anderson and Livingston modified this idea when studied the zero divisor graph that have vertices and for , edges if and only if . Many authors studied this notion see for examples [3], [4], [5] and [6] Recently, there are other concepts of zero divisor graph, see for examples [7], [8], [9] and In graph theory " denotes by the eccentricity of a vertex v of a connected graph G which is the number . That means is the distance between v and a vertex furthest from v. The radius of G ,which is denoted by is , while the diameter of G is the maximum eccentricity and it is denoted by .…”