Edge Domination Number on Graph Variations

Abstract

An edge dominating set D is a set of edges from the edge set E in graph G where every edge of $\langle E-D\rangle$ is adjacent to an element of $D$. Edge domination number is the cardinality of the smallest edge dominating set and is denoted by $\gamma ' (G)$. In this study, results for edge domination number of product graphs have been obtained and their algebraic properties have also been examined. Further, we introduce the concept of edge domination subdivision number and determine its value for some graphs and explore the relationship between edge domination subdivision number and edge domination number.