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The domination parameters of cubic graphs

Zverovich, Igor E.; Zverovich, Vadim

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Igor E. Zverovich


Let ir(G), γ(G), i(G), β0(G), Γ(G) and IR(G) be the irredundance number, the domination number, the independent domination number, the independence number, the upper domination number and the upper irredundance number of a graph G, respectively. In this paper we show that for any nonnegative integers k 1, k 2, k 3, k 4, k 5 there exists a cubic graph G satisfying the following conditions: γ(G) - ir(G) ≤ k 1, i(G) - γ(G) ≤ k 2, β0(G) - i(G) > k 3, Γ(G) - β0(G) - k 4, and IR(G) - Γ(G) - k 5. This result settles a problem posed in [9]. © Springer-Verlag 2005.


Zverovich, I. E., & Zverovich, V. (2005). The domination parameters of cubic graphs. Graphs and Combinatorics, 21(2), 277-288.

Journal Article Type Article
Publication Date Jun 1, 2005
Deposit Date Sep 24, 2015
Publicly Available Date Feb 19, 2016
Journal Graphs and Combinatorics
Print ISSN 0911-0119
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 21
Issue 2
Pages 277-288
Keywords cubic graphs, domination parameters
Public URL
Publisher URL
Additional Information Additional Information : The final publication is available at Springer via


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