Upper bounds for the bondage number of graphs on topological surfaces

Gagarin, A. and Zverovich, V. (2013) Upper bounds for the bondage number of graphs on topological surfaces. Discrete Mathematics, 313 (11). pp. 1132-1137. ISSN 0012-365X

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Publisher's URL: http://dx.doi.org/10.1016/j.disc.2011.10.018

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 D(G) and embeddable on an orientable surface of genus h and a non-orientable surface of genus k, b(G) <= min{D(G)+h+2, D(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.

Item Type:Article
Uncontrolled Keywords:bondage number, domination number, topological surface, embedding on a surface, Euler's formula
Faculty/Department:Faculty of Environment and Technology > Department of Engineering Design and Mathematics
~Pre-2012 Faculty Structure > Faculty of Environment and Technology > Department of Engineering Design and Mathematics
ID Code:16001
Deposited By: Dr V. Zverovich
Deposited On:21 Nov 2011 14:57
Last Modified:17 Apr 2013 04:15

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