SOME RESULTS ON THE MAXIMAL 2-RAINBOW DOMINATION NUMBER IN GRAPHS

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ABDOLLAHZADEH AHANGAR H.; GHANDALI Z.

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Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2016 | Volume:2 | Issue:7 Page(s): 13-20

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Title

SOME RESULTS ON THE MAXIMAL 2-RAINBOW DOMINATION NUMBER IN GRAPHS

Author(s)

ABDOLLAHZADEH AHANGAR H. | GHANDALI Z. | Issue Writer Certificate

Keywords

2-RAINBOW DOMINATING FUNCTIONQ1

2-RAINBOW DOMINATION NUMBERQ1

MAXIMAL 2-RAINBOW DOMINATING FUNCTIONQ1

MAXIMAL 2-RAINBOW DOMINATION NUMBERQ1

Abstract

A 2-RAINBOW DOMINATING FUNCTION (2RDF) of a graph G is a function F from the vertex set V(G) to the set of all subsets of the set {1, 2} such that for any vertex v Î V(G) with f(v)=Æ the condition ÈuÎN(v)f(u)={1, 2}is fulfilled, where N(v) is the open neighborhood of v. A maximal 2-RAINBOW DOMINATING FUNCTION on a graph G is a 2-RAINBOW DOMINATING FUNCTION f such that the set {wÎV(G)|f(w)=Æ} is not a dominating set of G. The weight of a maximal 2RDF f is the value w(f)=SvÎV|f(v)|. The maximal 2-RAINBOW DOMINATION NUMBER of a graph G, denoted by gmr(G), is the the minimum weight of a maximal 2RDF of G. In this paper, we continue the study of maximal 2-RAINBOW DOMINATION NUMBER. We characterize all graphs G of order n whose maximal 2-RAINBOW DOMINATION NUMBER is equal to 2 or 3. Finally, we characterize all graphs G of order n with g(G)³5 for which gm2r=n-2.

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APA: Copy

ABDOLLAHZADEH AHANGAR, H., & GHANDALI, Z.. (2016). SOME RESULTS ON THE MAXIMAL 2-RAINBOW DOMINATION NUMBER IN GRAPHS. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 2(7), 13-20. SID. https://sid.ir/paper/257302/en

Vancouver: Copy

ABDOLLAHZADEH AHANGAR H., GHANDALI Z.. SOME RESULTS ON THE MAXIMAL 2-RAINBOW DOMINATION NUMBER IN GRAPHS. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2016;2(7):13-20. Available from: https://sid.ir/paper/257302/en

IEEE: Copy

H. ABDOLLAHZADEH AHANGAR, and Z. GHANDALI, “SOME RESULTS ON THE MAXIMAL 2-RAINBOW DOMINATION NUMBER IN GRAPHS,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 2, no. 7, pp. 13–20, 2016, [Online]. Available: https://sid.ir/paper/257302/en

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