DOMINATION IN THE TOTAL GRAPH ON ℤn
2011 ◽
Vol 03
(04)
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pp. 413-421
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For a commutative ring R, let Z(R) be its set of zero-divisors. The total graph of R, denoted by TΓ(R), is the undirected graph with vertex set R, and for distinct x, y ∈ R, the vertices x and y are adjacent if and only if x + y ∈ Z(R). Tamizh Chelvam and Asir studied about the domination in the total graph of a commutative ring R. In particular, it was proved that the domination number γ(TΓ(ℤn)) = p1 where p1 is the smallest prime divisor of n. In this paper, we characterize all the γ-sets in TΓ(ℤn). Also, we obtain the values of other domination parameters like independent, total and perfect domination numbers of the total graph on ℤn.
2013 ◽
Vol 12
(04)
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pp. 1250198
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2012 ◽
Vol 11
(04)
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pp. 1250074
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2019 ◽
Vol 19
(05)
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pp. 2050089
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2013 ◽
Vol 12
(05)
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pp. 1250218
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2015 ◽
Vol 07
(01)
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pp. 1550004
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Keyword(s):
2020 ◽
Vol 24
(2)
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pp. 281-290
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