On the bondage number of middle graphs
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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.
Keywordsconnectivity network design and communication strong and weak domination number bondage number strong and weak bondage number middle graphs
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- 8.A. Mamut and E. Vumar, “A note on the integrity of middle graphs,” in Discrete Geometry, Combinatorics, and Graph Theory, Lecture Notes in Comput. Sci. (Springer-Verlag, Berlin, 2007), Vol. 4381, pp. 130–134.Google Scholar