Criticality indices of 2-rainbow domination of paths and cycles

• Autorzy: Bouchou A. , Blidia M.

Identyfikatory

DOI

10.7494/OpMath.2016.36.5.563

• Języki publikacji: EN

Abstrakty

EN

A 2-rainbow dominating function of a graph G (V(G), E(G)) is a function ƒ that assigns to each vertex a set of colors chosen from the set {1,2} so that for each vertex with ƒ (v) = ∅ we have [formula].The weight of a 2RDF ƒ is defined as [formula] minimum weight of a 2RDF is called the 2-rainbow domination number of G, denoted by [formula].The vertex criticality index of a 2-rainbow domination of a graph G is defined as [formula] the edge removal criticality index of a 2-rainbow domination of a graph G is defined as [formula] and the edge addition of a 2-rainbow domination criticality index of G is defined as [formula] where G is the complement graph of G. In this paper, we determine the criticality indices of paths and cycles.

Słowa kluczowe

EN

2-rainbow domination number; criticality index

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2016
• Tom: Vol. 36, no. 5
• Strony: 563--–574
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Bouchou A.

• University of Medea, Algeria

autor

Blidia M.

• University of Blida LAMDA-RO, Department of Mathematics B.P. 270, Blida, Algeria

Bibliografia

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• [7] N. Jafari Rad, Critical concept for 2-rainbow domination in graphs, Australasian Journal of Combinatorics 51 (2011), 49-60.
• [8] N. Jafari Rad, L. Volkmann, Changing and unchanging the Roman domination number of a graph, Utilitas Mathematica 89 (2012), 79-95.
• [9] D.P. Sumner, P. Blitch, Domination critical graphs, J. Combin. Theory Ser. B 34 (1983), 65-76.
• [10] H.B. Walikar, B.D. Acharya, Domination critical graphs, Nat. Acad. Sci. Lett. 2 (1979), 70-72.
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Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.