THE ZERO-DIVISOR GRAPHS OF RINGS AND SEMIRINGS
2012 ◽
Vol 22
(04)
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pp. 1250033
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In this paper we study zero-divisor graphs of rings and semirings. We show that all zero-divisor graphs of (possibly noncommutative) semirings are connected and have diameter less than or equal to 3. We characterize all acyclic zero-divisor graphs of semirings and prove that in the case zero-divisor graphs are cyclic, their girths are less than or equal to 4. We find all possible cyclic zero-divisor graphs over commutative semirings having at most one 3-cycle, and characterize all complete k-partite and regular zero-divisor graphs. Moreover, we characterize all additively cancellative commutative semirings and all commutative rings such that their zero-divisor graph has exactly one 3-cycle.
2011 ◽
Vol 10
(04)
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pp. 665-674
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2019 ◽
Vol 19
(12)
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pp. 2050226
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2012 ◽
Vol 55
(1)
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pp. 127-137
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2011 ◽
Vol 27
(6)
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pp. 1221-1232
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2020 ◽
Vol 12
(1)
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pp. 84-101
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2016 ◽
Vol 09
(04)
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pp. 1650071
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2014 ◽
Vol 34
(1)
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pp. 45