Upper bounds for the bondage number of graphs on topological surfaces

Andrei Gagarin; Vadim Zverovich

doi:10.1016/j.disc.2011.10.018

Upper bounds for the bondage number of graphs on topological surfaces

Combinatorics 2016-04-25 v2 Discrete Mathematics

Authors: Andrei Gagarin , Vadim Zverovich

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Abstract

The bondage number b(G) of a graph G is the smallest number of edges of G whose removal from G 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 $\Delta(G)$ and embeddable on an orientable surface of genus h and a non-orientable surface of genus k, $b(G)\le \min\{\Delta(G)+h+2, \Delta(G)+k+1\}$ . This generalizes known upper bounds for planar and toroidal graphs.

Keywords

bondage number domination number graph embedding topological surface upper bound orientable surface non-orientable surface

Cite

@article{arxiv.1012.4117,
  title  = {Upper bounds for the bondage number of graphs on topological surfaces},
  author = {Andrei Gagarin and Vadim Zverovich},
  journal= {arXiv preprint arXiv:1012.4117},
  year   = {2016}
}

Comments

10 pages; Updated version (April 2011); Presented at the 7th ECCC, Wolfville (Nova Scotia, Canada), May 4-6, 2011, and the 23rd BCC, Exeter (England, UK), July 3-8, 2011

Upper bounds for the bondage number of graphs on topological surfaces

Abstract

Keywords

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