Edge Cut Domination, Irredundance, and Independence in Graphs

Abstract

An edge dominating set $F$ of a graph $G=(V,E)$ is an \textit{edge cut dominating set} if the subgraph $⟨V,G-F⟩$ is disconnected. The \textit{edge cut domination number} ${\gamma }_{ct}(G)$ of $G$ is the minimum cardinality of an edge cut dominating set of $G.$ In this paper we study the edge cut domination number and investigate its relationships with other parameters of graphs. We also introduce the properties edge cut irredundance and edge cut independence.