Classification of rings with toroidal co-annihilating-ideal graphs
Let [Formula: see text] be a commutative ring with identity. The co-annihilating-ideal graph of [Formula: see text], denoted by [Formula: see text], is a graph whose vertex set is the set of all nonzero proper ideals of [Formula: see text] and two distinct vertices [Formula: see text] and [Formula: see text] are adjacent whenever [Formula: see text]. In this paper, we study the planarity and genus of [Formula: see text]. In particular, we characterize all Artinian rings [Formula: see text] for which the genus of [Formula: see text] is zero or one.
Keyword(s):
2012 ◽
Vol 11
(03)
◽
pp. 1250049
◽
Keyword(s):
2018 ◽
Vol 17
(07)
◽
pp. 1850125
Keyword(s):
Keyword(s):
2014 ◽
Vol 14
(01)
◽
pp. 1550008
◽
Keyword(s):
2013 ◽
Vol 12
(04)
◽
pp. 1250199
◽