Edge irregular reflexive labeling for star, double star and caterpillar graphs

Abstract

A graph labeling is an algorithm that assignment the labels, traditionally represented by integers, to the edges or vertices, or both, of a network(graph) G. Formally, given a graph G = (V, E), a vertex labeling is a function of V to a set of labels. A graph with such a function defined is called a vertex-labeled graph. Likewise, an edge labeling is a function of E to a set of labels. In this case, the graph is called an edgelabeled graph. We study an edge irregular reflexive k−labeling for the star, double star and caterpillar graphs and determine the exact value of the reflexive edge strength for these graphs.