Edge Cut Domination, Irredundance, and Independence in Graphs

TL;DR

This paper introduces and studies the edge cut domination number in graphs, exploring its properties and relationships with other graph parameters, and also defines related concepts like edge cut irredundance and independence.

Contribution

It presents the concept of edge cut domination number, analyzes its properties, and introduces new related parameters such as edge cut irredundance and independence.

Findings

Defined the edge cut domination number and its properties

Explored relationships with existing graph parameters

Introduced edge cut irredundance and independence concepts

Abstract

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.