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A generalised upper bound for the k-tuple domination number

Gagarin, Andrei; Zverovich, Vadim

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Authors

Andrei Gagarin



Abstract

In this paper, we provide an upper bound for the k-tuple domination number that generalises known upper bounds for the double and triple domination numbers. We prove that for any graph G,γ× k (G) ≤ frac(ln (δ - k + 2) + ln (∑m = 1k - 1 (k - m) over(d, ^)m + ε{lunate}) + 1, δ - k + 2) n,where γ× k (G) is the k-tuple domination number; δ is the minimal degree; over(d, ^)m is the m-degree of G; ε{lunate} = 1 if k = 1 or 2 and ε{lunate} = - d if k ≥ 3; d is the average degree. © 2007 Elsevier B.V. All rights reserved.

Citation

Gagarin, A., & Zverovich, V. (2008). A generalised upper bound for the k-tuple domination number. Discrete Mathematics, 308(5-6), 880-885. https://doi.org/10.1016/j.disc.2007.07.033

Journal Article Type Article
Publication Date Mar 28, 2008
Deposit Date Nov 12, 2010
Publicly Available Date Nov 15, 2016
Journal Discrete Mathematics
Print ISSN 0012-365X
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 308
Issue 5-6
Pages 880-885
DOI https://doi.org/10.1016/j.disc.2007.07.033
Keywords graph, domination
Public URL https://uwe-repository.worktribe.com/output/1018614
Publisher URL http://dx.doi.org/10.1016/j.disc.2007.07.033

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