Andrei Gagarin
Upper bounds for α-domination parameters
Gagarin, Andrei; Poghosyan, Anush; Zverovich, Vadim
Abstract
We provide a new upper bound for the α-domination number in terms of a parameter α, 0 < α ≤ 1, and graph vertex degrees. This result generalises the well-known Caro-Roditty bound for the domination number of a graph. The same probabilistic construction is used to generalise another well-known upper bound for the classical domination in graphs. Using a different probabilistic construction, we prove similar upper bounds for the α-rate domination number, which combines the concepts of α-domination and k-tuple domination. © Springer-Verlag 2009.
Citation
Gagarin, A., Poghosyan, A., & Zverovich, V. (2009). Upper bounds for α-domination parameters. Graphs and Combinatorics, 25(4), 513-520. https://doi.org/10.1007/s00373-009-0864-6
Journal Article Type | Article |
---|---|
Publication Date | Dec 1, 2009 |
Deposit Date | Nov 12, 2010 |
Publicly Available Date | Oct 27, 2016 |
Journal | Graphs and Combinatorics |
Print ISSN | 0911-0119 |
Publisher | Springer Verlag |
Peer Reviewed | Peer Reviewed |
Volume | 25 |
Issue | 4 |
Pages | 513-520 |
DOI | https://doi.org/10.1007/s00373-009-0864-6 |
Keywords | graph, domination, α-Domination, α-rate domination, probabilistic method |
Public URL | https://uwe-repository.worktribe.com/output/1002607 |
Publisher URL | http://dx.doi.org/10.1007/s00373-009-0864-6 |
Additional Information | Additional Information : The original publication is available at http://dx.doi.org/10.1007/s00373-009-0864-6 |
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