The cototal domination number of a graph

Kulli, V. R.; Janakiram, B.; Iyer, Radha Rajamani

doi:10.1080/09720529.1999.10697889

Cited by 34 publications

(36 citation statements)

References 3 publications

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“…6 , v 10 } is a minimum eccentric dominating set. 6 , v 10 } is a minimum complementary nil eccentric dominating set. Here D = {v 2 , v 4 , v 5 } is a minimum complementary nil eccentric dominating set.…”

Section: Resultsmentioning

confidence: 99%

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Complementary Nil Eccentric Domination Number of a Graph

Bhanumathi¹,

Senthil²

2016

International Journal of Mathematics and Soft Computing

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A subset D of the vertex set V (G) of a graph G is said to be a dominating set if every vertex not in D is adjacent to atleast one vertex in D. A dominating set D is said to be an eccentric dominating set if for every v ∈ V − D, there exists atleast one eccentric point of v in D. An eccentric dominating set D of G is a complementary nil eccentric dominating set if the induced subgraph < V − D > is not an eccentric dominating set for G. The minimum of the cardinalities of the complementary nil eccentric dominating sets of G is called the complementary nil eccentric domination number γ cned (G) of G. In this paper, bounds for γ cned (G), its exact value for some particular classes of graphs and some results on complementary nil eccentric domination number are obtained.

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Section: Resultsmentioning

confidence: 99%

“…Kulli and Janakiram introduced the maximal domination number in graphs [6]. This maximal domination is also termed as complementary nil domination.…”

Section: Introductionmentioning

confidence: 99%

Complementary Nil Eccentric Domination Number of a Graph

Bhanumathi¹,

Senthil²

2016

International Journal of Mathematics and Soft Computing

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“…Nordhaus-Gaddum type results are also obtained for this new parameter. Kulli and Janakiram (2003) also introduced the concept of strong non-split domination number in graphs. A dominating set D of a Graph is a strong non-split dominating set, if the induced subgraph <V-D> is complete and connected.…”

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confidence: 99%

The inverse strong non-split r-domination number of a graph

Ameenal¹,

Selvakumar²

2010

Int. J. Eng. Sci. Tech

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In this paper, we define the notions of inverse strong non-split r-dominating set and inverse strong non-split r-domination number γ′ sns r(G) of a graph G. We characterize graphs for which γ sns r(G) + γ′ sns r(G) = n, where γ sns r(G) is the strong non-split r-domination number of G. We get many bounds on γ′ sns r(G). Nordhaus-Gaddum type results are also obtained for this new parameter.Keywords: r-independent set, r-dominating set, strong non-split r-dominating set, inverse strong non-split r-dominating set, strong non-split r-domination number and inverse strong non-split r-domination number.

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“…The various bounds of global domination number in terms of order, degrees and domination number of graph is given by Brigham and Duttom [1]. The global domination number for one-point union of finite number of copies of cycles C n is reported in Vaidya and Pandit [5] while Kulli and Janakiram [3] have introduced the concept of total global dominating sets.…”

Section: Introductionmentioning

confidence: 99%