Finite commutative rings with higher genus unit graphs
2014 ◽
Vol 14
(01)
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pp. 1550002
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Let R be a ring with identity. The unit graph of R, denoted by G(R), is a simple graph with vertex set R, and where two distinct vertices x and y are adjacent if and only if x + y is a unit in R. The genus of a simple graph G is the smallest nonnegative integer g such that G can be embedded into an orientable surface Sg. In this paper, we determine all isomorphism classes of finite commutative rings whose unit graphs have genus at most three.
2014 ◽
Vol 06
(03)
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pp. 1450037
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2013 ◽
Vol 12
(04)
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pp. 1250199
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2018 ◽
Vol 17
(07)
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pp. 1850121
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2012 ◽
Vol 11
(06)
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pp. 1250103
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2020 ◽
Vol 12
(1)
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pp. 84-101
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Keyword(s):
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2016 ◽
Vol 08
(02)
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pp. 1650029
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Keyword(s):
2018 ◽
Vol 17
(10)
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pp. 1850193
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Keyword(s):
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