Minus domination in regular graphs

Dunbar, Jean E.; Hedetniemi, Stephen T.; Henning, Michael A.; McRae, Alice A.

doi:10.1016/0012-365x(94)00329-h

Cited by 57 publications

(45 citation statements)

References 2 publications

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“…Zelinka [29] established a sharp lower bound on γ − (G) for a cubic graph G. Dunbar, et al [47] generalized this result to k-regular graphs. They showed that γ − (G) n/(k + 1) for a k-regular graph G of order n. In 2000, Kang and Shan [21] further generalized this result to a general graph.…”

Section: Minus Domination In Graphsmentioning

confidence: 96%

Dominating functions with integer values in graphs—a survey

Kang

Shan

2007

J. of Shanghai Univ.

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For an arbitrary subset P of the reals, a function f : V → P is defined to be a P-dominating function of a graph G = (V, E) if the sum of its function values over any closed neighbourhood is at least 1. That is, for everyThe definition of total P-dominating function is obtained by simply changing 'closed' neighborhood N [v] in the definition of P-dominating function to 'open' neighborhood N (v). The (total) P-domination number of a graph G is defined to be the infimum of weight w(f ) = P v∈V f (v) taken over all (total) P-dominating function f . Similarly, the P-edge and P-star dominating functions can be defined. In this paper we survey some recent progress on the topic of dominating functions in graph theory. Especially, we are interested in P-, P-edge and P-star dominating functions of graphs with integer values.

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Section: Minus Domination In Graphsmentioning

confidence: 96%

Dominating functions with integer values in graphs—a survey

Kang

Shan

2007

J. of Shanghai Univ.

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“…Our definitions are based on those defined in [2,3,6,7]. A signed dominating function [6] is an opinion function such that the sum of the opinions in each closed neighborhood is positive (every vertex votes aye).…”

Section: Introductionmentioning

confidence: 99%

“…A signed dominating function [6] is an opinion function such that the sum of the opinions in each closed neighborhood is positive (every vertex votes aye). The signed domination number of G is the minimum weight of a signed dominating function on G. A majority dominating function [7] is an opinion function for which at least half the vertices vote aye, and the minimum weight of such a function is the majority domination number.…”

Section: Introductionmentioning

confidence: 99%

Strict majority functions on graphs

Henning

Hind

1998

J. Graph Theory

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“…If A ⊆ V (G) and f is a mapping from V (G) into some set of numbers, then f (A) = ∑ x∈A f (x). A signed dominating function is defined in [1] as a two-valued function f :…”

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confidence: 99%