ABSTRACT
This chapter characterizes a restrained edge dominating set and also investigates a restrained edge domination number of book graph, crown, armed crown, and friendship graph. The concept of domination in a graph is one of the fastest growing areas within and outside of graph theory. The chapter considers a simple, finite, connected and undirected graph of a specific order. It provides information on an edge analogue of restrained domination in graphs. The chapter discusses the restrained edge domination number of star related graphs and cycle related graphs. The concept of restrained edge domination is a variant of restrained domination and edge domination. The restrained edge dominating set relates the edge set and its complement.
