Signed domination in regular graphs

Favaron, Odile

doi:10.1016/0012-365x(96)00026-x

Cited by 72 publications

(38 citation statements)

References 2 publications

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“…Subsequently, Zelinka [29] showed that for every cubic graph G of order n, γ s (G) 4n/5. Favaron [16] improved Zelinka's result. She showed that every cubic graph of order n different from the Petersen graph has signed domination number at most 3n/4.…”

Section: Signed Domination In Graphsmentioning

confidence: 54%

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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: Signed Domination In Graphsmentioning

confidence: 54%

“…Signed domination has been studied in [7,[14][15][16][17][18][19][20][21][22][23][24][25][26][27] and elsewhere.…”

Section: Signed Domination In Graphsmentioning

confidence: 99%

Dominating functions with integer values in graphs—a survey

Kang

Shan

2007

J. of Shanghai Univ.

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“…Further we studied about signed domination in [2,7]. In 1996, Favaron [5] have studied about "Signed domination in regular graphs". In 2010, Zhong-sheng [3] have studied about "On Inverse Signed Total Domination in Graphs".…”

Section: G G mentioning

confidence: 99%

Inverse Signed Dominating Functions of Corona and Rooted Product Graphs

Rani¹

2017

ijarcs

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Abstract:Graph theory is an interesting subject in mathematics. Applications in many fields like Linguistics, Engineering communications, Physical Sciences, Coding theory, Computer networking and Logical Algebra. The theory of domination in graphs has a wide range of applications. Among these applications, the most often discussed is a coding theory and communication networks. Inverse domination theory of graphs which are the important branches of graph theory. In this paper, we study the maximal inverse signed dominating functions of corona product graph of a path with a complete graph and rooted product graph of a path with a cycle.

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“…of G is the minimum weight of a signed domination function on G. In [1] Dunbar introduced this concept and it has been studied by several authors, see [1][2][3][4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

A lower bound on the total signed domination numbers of graphs

2007

SCI CHINA SER A

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Signed domination in regular graphs

Cited by 72 publications

References 2 publications

Dominating functions with integer values in graphs—a survey

Dominating functions with integer values in graphs—a survey

Inverse Signed Dominating Functions of Corona and Rooted Product Graphs

A lower bound on the total signed domination numbers of graphs

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