TY - JOUR
ID - 13555
TI - The sum-annihilating essential ideal graph of a commutative ring
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - Alilou, Abbas
AU - Amjadi, Jafar
AD - Azarbaijan Shahid Madani University
Y1 - 2016
PY - 2016
VL - 1
IS - 2
SP - 117
EP - 135
KW - Commutative rings
KW - annihilating ideal
KW - essential ideal
KW - genus of a graph
DO - 10.22049/cco.2016.13555
N2 - Let $R$ be a commutative ring with identity. An ideal $I$ of a ring $R$ is called an annihilating ideal if there exists $rin Rsetminus {0}$ such that $Ir=(0)$ and an ideal $I$ of $R$ is called an essential ideal if $I$ has non-zero intersection with every other non-zero ideal of $R$. The sum-annihilating essential ideal graph of $R$, denoted by $mathcal{AE}_R$, is a graph whose vertex set is the set of all non-zero annihilating ideals and two vertices $I$ and $J$ are adjacent whenever ${rm Ann}(I)+{rm Ann}(J)$ is an essential ideal. In this paper we initiate the study of the sum-annihilating essential ideal graph. We first characterize all rings whose sum-annihilating essential ideal graph are stars or complete graphs and then establish sharp bounds on domination number of this graph. Furthermore determine all isomorphism classes of Artinian rings whose sum-annihilating essential ideal graph has genus zero or one.
UR - http://comb-opt.azaruniv.ac.ir/article_13555.html
L1 - http://comb-opt.azaruniv.ac.ir/article_13555_3f74eb186e2bee9fefcb8aa541b1f23c.pdf
ER -