5 research outputs found
On the Diameter and Girth of an Annihilating-Ideal Graph
Let be a commutative ring with and be the set of
ideals with nonzero annihilators. The annihilating-ideal graph of is
defined as the graph with the vertex set and two distinct vertices and are adjacent
if and only if . In this paper, we first study the interplay between
the diameter of annihilating-ideal graphs and zero-divisor graphs. Also, we
characterize rings when , and so we
characterize rings whose annihilating-ideal graphs are bipartite. Finally, in
the last section we discuss on a relation between the Smarandache vertices and
diameter of .Comment: 11 pages, 1 figur