Mathematical Notes

, Volume 93, Issue 5–6, pp 795–801 | Cite as

On the bondage number of middle graphs

Article

Abstract

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 vV (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.

Keywords

connectivity network design and communication strong and weak domination number bondage number strong and weak bondage number middle graphs 

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Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Ege UniversityEgeTurkey
  2. 2.Izmir University of EconomicsIzmirTurkey

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