@article {
author = {Krishnan, Selvakumar and P, Subbulakshmi},
title = {Classification of rings with toroidal annihilating-ideal graph},
journal = {Communications in Combinatorics and Optimization},
volume = {3},
number = {2},
pages = {93-119},
year = {2018},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2018.26060.1072},
abstract = {Let $R$ be a non-domain commutative ring with identity and $A^*(R)$ be the set of non-zero ideals with non-zero annihilators. We call an ideal $I$ of $R$, an annihilating-ideal if there exists a non-zero ideal $J$ of $R$ such that $IJ =(0)$. The annihilating-ideal graph of $R$ is defined as the graph $AG(R)$ with the vertex set $A^*(R)$ and two distinct vertices $I$ and $J$ are adjacent if and only if $IJ =(0)$. In this paper, we characterize all commutative Artinian nonlocal rings $R$ for which $AG(R)$ has genus one. },
keywords = {annihilating-ideal,planar,genus,local ring,annihilating-ideal graph},
url = {http://comb-opt.azaruniv.ac.ir/article_13745.html},
eprint = {http://comb-opt.azaruniv.ac.ir/article_13745_64b16e21db453555d1fe39afe192d7e5.pdf}
}