The domination parameters of cubic graphs

Zverovich, Igor E.; Zverovich, Vadim

Abstract

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.

Citation

Zverovich, V. E., Zverovich, I. E., Zverovich, I., & Zverovich, V. (2005). The domination parameters of cubic graphs. Graphs and Combinatorics, 21(2), 277-288. https://doi.org/10.1007/s00373-005-0608-1

• Journal Article Type: Article
• Publication Date: Jun 1, 2005
• Journal: Graphs and Combinatorics
• Print ISSN: 0911-0119
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 21
• Issue: 2
• Pages: 277-288
• DOI: https://doi.org/10.1007/s00373-005-0608-1
• Keywords: cubic graphs, domination parameters
• Public URL: https://uwe-repository.worktribe.com/output/1056441
• Publisher URL: http://dx.doi.org/10.1007/s00373-005-0608-1
• Additional Information: Additional Information : The final publication is available at Springer via http://dx.doi.org/10.1007/s00373-005-0608-1