Upper bounds for domination related parameters in graphs on surfaces

Abstract

In this paper we give tight upper bounds on the total domination number, the weakly connected domination number and the connected domination number of a graph in terms of order and Euler characteristic. We also present upper bounds for the restrained bondage number, the total restrained bondage number and the restricted edge connectivity of graphs in terms of the orientable/nonorientable genus and maximum degree.

Keywords

• Total/(weakly) connected domination number
• (Total) restrained/Roman bondage number
• Euler characteristic
• Orientable/nonorientable genus