CN-edge domination in graphs

Alwardi A. , Soner N.D.
Vladikavkaz Mathematical Journal 2013. Vol. 15. Issue 2.

Abstract:
Let \(G=(V,E)\) be a graph. A subset \(D\) of \(V\) is called common neighbourhood  dominating set (CN-dominating set) if for every \(v\in V-D\) there exists a vertex \(u\in D\) such that \(uv\in E(G\)$  and \(|\Gamma(u,v)|\geq1\), where \(|\Gamma(u,v)|\) is the number of common neighbourhood between the vertices\(u\) and \(v\). The minimum cardinality of such CN-dominating set denoted by \(\gamma_{cn}(G)\) and is called common neighbourhood domination number (CN-edge domination).

Keywords: common neighbourhood edge dominating set, common neighbourhood edge domatic number, common neighbourhood edge domination number

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