Cototal edge domination number of a graph

Abstract

A set \(F\) of a graph \(G(V, E)\) is an edge dominating set if every edge in \(E-F\) is adjacent to some edge in \(F\). An edge domination number \(\gamma^{\prime}(G)\) of \(G\) is the minimum cardinality of an edge dominating set. An edge dominating set \(F\) is called a cototal edge dominating set if the induced subgraph \(\langle E-F\rangle\) doesnot contain isolated edge. The minimum cardinality of the cototal edge dominating set in \(G\) is its domination number and is denoted by \(\gamma_{c o t}^{\prime}(G)\). We investigate several properties of cototal edge dominating sets and give some bounds on the cototal edge domination number.