Special Kinds of Domination Parameters of Edge-Deleted Graphs

We study the behaviour of two domination parameters: the split domination number \(\gamma_s(G)\) of a graph \(G\) and the maximal domination number \(\gamma_m(G)\) of \(G\) after the deletion of an edge from \(G\). The motivation of these problems comes from [2]. In [6] Vizing gave an upper bound for the size of a graph with a given domination number. Inspired by [5] we formulate Vizing type relation between \(|E(G)|, |V(G)|, \Delta(G)\) and \(\delta(G)\), where \(\Delta(G)\) (\(\delta(G)\)) denotes the maximum (minimum) degree of \(G\).