On the bondage number of middle graphs. (English. Russian original) Zbl 1269.05086
Math. Notes 93, No. 6, 795-801 (2013); translation from Mat. Zametki 93, No. 6, 803-811 (2013).
Summary: 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 \(v\in V(G)-S\), there exists some vertex \(u\in S\) such that \(uv\in E(G)\). The domination number, denoted by \(\gamma(G)\), 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.
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.
MSC:
| 05C69 | Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) |
| 05C40 | Connectivity |
Keywords:
connectivity; network design and communication; strong and weak domination number; bondage number; strong and weak bondage number; middle graphsReferences:
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