  An edge dominating set $F$ of a graph $G=(V,E)$ is an \textit{edge cut
dominating set} if the subgraph $\langle V,G-F \rangle$ 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.
