The bondage number of some graphs

Abstract

The stability of a communication network, composed of processing nodes and communication links, is of prime importance to network designers. On description of the network resistance, finding critical vertices or links, are written many papers. In 1970s different measures of the graph vulnerability are introduced to study different aspects of the graph behaviour after removal of vertices or links. The domination number is one of these measures. Different types of domination parameters are defined such as bondage, reinforcement, strong-weak domination, strong-weak bondage numbers. In this paper, firstly we investigate strong-weak domination number of corona and gear graphs. Then several results for the bondage, strong-weak bondage of corona and gear graphs are obtained.