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. For- mally, 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 edge- labeled graph. We study an edge irregular re exive k-labeling for the star, double star and caterpillar graphs and determine the exact value of the re exive edge strength for these graphs.