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Upper bounds for the bondage number of graphs on topological surfaces

Gagarin, Andrei; Zverovich, Vadim

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Authors

Andrei Gagarin



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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