The genus two class of graphs arising from rings
2018 ◽
Vol 17
(10)
◽
pp. 1850193
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Keyword(s):
Given a commutative ring [Formula: see text] with identity [Formula: see text], its Jacobson graph [Formula: see text] is defined to be the graph in which the vertex set is [Formula: see text], and two distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text]. Here [Formula: see text] denotes the Jacobson radical of [Formula: see text] and [Formula: see text] is the set of unit elements in [Formula: see text]. This paper investigates the genus properties of Jacobson graph. In particular, we determine all isomorphism classes of commutative rings whose Jacobson graph has genus two.
2012 ◽
Vol 12
(03)
◽
pp. 1250179
◽
2018 ◽
Vol 17
(07)
◽
pp. 1850121
Keyword(s):
2018 ◽
Vol 17
(09)
◽
pp. 1850168
Keyword(s):
2014 ◽
Vol 06
(03)
◽
pp. 1450037
Keyword(s):
2012 ◽
Vol 11
(03)
◽
pp. 1250049
◽
Keyword(s):
2019 ◽
Vol 11
(01)
◽
pp. 1950010
Keyword(s):
2013 ◽
Vol 12
(04)
◽
pp. 1250199
◽
Keyword(s):
Keyword(s):
2019 ◽
Vol 13
(07)
◽
pp. 2050121
Keyword(s):