Upper bounds for the bondage number of graphs on topological surfaces

Details Upper bounds for the bondage number of graphs on topological surfaces Upper bounds for the bondage number of graphs on topological surfaces

2010-12-18

arxiv.org/abs/1012.4117v2

Mathematics

Combinatorics

10 pages; Updated version (April 2011); Presented at the 7th ECCC, Wolfville (Nova Scotia, Canada), May 4-6, 2011, and the 23r

Scientific paper

10.1016/j.disc.2011.10.018

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.

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