BOUNDING THE RAINBOW DOMINATION NUMBER OF A TREE IN TERMS OF ITS ANNIHILATION NUMBER

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DEHGARDI N.; SHEIKHOLESLAMI S.M.; KHODKAR ABDOLLAH

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ISSN: 2588-4824

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Journal: TRANSACTIONS ON COMBINATORICS Year:2013 | Volume:2 | Issue:3 Page(s): 21-32

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Title

BOUNDING THE RAINBOW DOMINATION NUMBER OF A TREE IN TERMS OF ITS ANNIHILATION NUMBER

Author(s)

DEHGARDI N. | SHEIKHOLESLAMI S.M. | KHODKAR ABDOLLAH | Issue Writer Certificate

Keywords

ANNIHILATION NUMBERQ2

2-RAINBOW DOMINATING FUNCTIONQ2

2-RAINBOW DOMINATION NUMBERQ2

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 vÎV (G) with f (v) = f the condition UuÎN (v) f (u) = {1, 2} is fulfilled, where N (v) is the open neighborhood of v. The weight of a 2RDF f is the value w (f) = SvÎV |f (v) |. The 2-RAINBOW DOMINATION NUMBER of a graph G, denoted by yr2 (G), is the minimum weight of a 2RDF of G. The ANNIHILATION NUMBER a (G) is the largest integer k such that the sum of the first k terms of the non-decreasing degree sequence of G is at most the number of edges in G. In this paper, we prove that for any tree T with at least two vertices, yr2 (T) £ a (T) +1.

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APA: Copy

DEHGARDI, N., SHEIKHOLESLAMI, S.M., & KHODKAR, ABDOLLAH. (2013). BOUNDING THE RAINBOW DOMINATION NUMBER OF A TREE IN TERMS OF ITS ANNIHILATION NUMBER. TRANSACTIONS ON COMBINATORICS, 2(3), 21-32. SID. https://sid.ir/paper/213747/en

Vancouver: Copy

DEHGARDI N., SHEIKHOLESLAMI S.M., KHODKAR ABDOLLAH. BOUNDING THE RAINBOW DOMINATION NUMBER OF A TREE IN TERMS OF ITS ANNIHILATION NUMBER. TRANSACTIONS ON COMBINATORICS[Internet]. 2013;2(3):21-32. Available from: https://sid.ir/paper/213747/en

IEEE: Copy

N. DEHGARDI, S.M. SHEIKHOLESLAMI, and ABDOLLAH KHODKAR, “BOUNDING THE RAINBOW DOMINATION NUMBER OF A TREE IN TERMS OF ITS ANNIHILATION NUMBER,” TRANSACTIONS ON COMBINATORICS, vol. 2, no. 3, pp. 21–32, 2013, [Online]. Available: https://sid.ir/paper/213747/en

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