Pendant Edge Domination in Graphs

Abstract

A dominating set of a graph $G$ is said to be pendant dominating set if the induced subgraph contains at least one pendant vertex. A subset $F$ of edges of $G$ is said to be an edge dominating set if every edge not in $F$ is incident to at least one edge in $F$. An edge dominating set is said to be pendant edge dominating set if an edge induced subgraph $\langle F\rangle$ contains an edge of degree one. In this article, we initiate the study of pendant edge domination of graph and compute exact values for some standard graphs.