Author/Authors :
Ahrari, M. Department of Mathematics - Islamic Azad University, Central Tehran Branch , Safari Sabet, Sh. A. Department of Mathematics - Islamic Azad University, Central Tehran Branch , Amini, B. Department of Mathematics - College of Sciences, Shiraz University
Abstract :
The annihilating-ideal graph of a commutative ring R is denoted by AG(R), whose
vertices are all nonzero ideals of R with nonzero annihilators and two distinct vertices I and
J are adjacent if and only if IJ = 0. In this article, we completely characterize rings R when
gr(AG(R)) ̸= 3.
Keywords :
Annihilating-ideal graph , star graph , bipartite graph , girth
