Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/15143
Title: Proof of a conjecture on k-tuple domination in graphs
Authors: Xu, G
Kang, L
Shan, E
Yan, H 
Keywords: Domination
k-tuple domination
Probabilistic method
Issue Date: 2008
Publisher: Pergamon Press
Source: Applied mathematics letters, 2008, v. 21, no. 3, p. 287-290 How to cite?
Journal: Applied mathematics letters 
Abstract: Let G = (V, E) be a graph and N G [v] the closed neighborhood of a vertex v in G. For k ∈ N, the minimum cardinality of a set D ⊆ V with | N G [v] ∩ D | ≥ k for all v ∈ V is the k-tuple domination number γ × k (G) of G. In this note we prove the following conjecture of Rautenbach and Volkmann [D. Rautenbach, L. Volkmann, New bounds on the k-domination number and the k-tuple domination number, Appl. Math. Lett. 20 (2007) 98-102]: If k ∈ N and G = (V, E) is a graph of order n and minimum degree δ ≥ k, then γ × k (G) ≤ frac(n, δ + 2 - k) (ln (δ + 2 - k) + ln (under(∑, v ∈ V) (frac(d G (v) + 1, k - 1))) - ln (n) + 1) .
URI: http://hdl.handle.net/10397/15143
ISSN: 0893-9659
DOI: 10.1016/j.aml.2007.03.015
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