Andrei Gagarin
Upper bounds for the bondage number of graphs on topological surfaces
Gagarin, Andrei; Zverovich, Vadim
Abstract
The bondage number b(G) of a graph G is the smallest number of edges of G whose removal results in a graph having the domination number larger than that of G. We show that, for a graph G having the maximum vertex degree Δ(G) and embeddable on an orientable surface of genus h and a non-orientable surface of genus k, b(G)≤min{Δ(G)+h+2,Δ(G)+k+1}. This generalizes known upper bounds for planar and toroidal graphs, and can be improved for bigger values of the genera h and k by adjusting the proofs. © 2011 Elsevier B.V. All rights reserved.
Citation
Gagarin, A., & Zverovich, V. (2013). Upper bounds for the bondage number of graphs on topological surfaces. Discrete Mathematics, 313(11), 1132-1137. https://doi.org/10.1016/j.disc.2011.10.018
Journal Article Type | Article |
---|---|
Publication Date | Jan 1, 2013 |
Publicly Available Date | Jun 7, 2019 |
Journal | Discrete Mathematics |
Print ISSN | 0012-365X |
Publisher | Elsevier |
Peer Reviewed | Peer Reviewed |
Volume | 313 |
Issue | 11 |
Pages | 1132-1137 |
DOI | https://doi.org/10.1016/j.disc.2011.10.018 |
Keywords | bondage number, domination number, topological surface, embedding on a surface, Euler's formula |
Public URL | https://uwe-repository.worktribe.com/output/931020 |
Publisher URL | http://dx.doi.org/10.1016/j.disc.2011.10.018 |
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