Upper bounds for the bondage number of graphs on topological surfaces

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.

arXiv comment10 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

Cited by in corpus (3)

• An improved upper bound for the bondage number of graphs on surfaces
• The bondage number of graphs on topological surfaces and Teschner's conjecture
• On Bondage Numbers of Graphs -- a survey with some comments