On the bondage number of middle graphs
Aysun Aytaç, Tufan Turacı, Zeynep Nihan Odabaş · Mathematical Notes · 2013
Let G = ( V ( G ), E ( G )) be a simple graph. A subset S of V ( G ) is a dominating set of G if, for any vertex v ∈ V ( G ) — S , there exists some vertex u ∈ S such that uv ∈ E ( G ). The domination number, denoted by γ ( G ), is the cardinality of a minimal dominating set of G . There are several types of domination parameters depending upon the nature of domination and the nature of dominating set. These parameters are bondage, reinforcement, strong-weak domination, strong-weak bondage numbers. In this paper, we first investigate the strong-weak domination number of middle graphs of a graph. Then several results for the bondage, strong-weak bondage number of middle graphs are obtained.