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
Unable to display preview. Download preview PDF.
- 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