Edge Reflexive Irregularity Strength of -graphs

Abstract

The labeling of a simple finite graph J is allocation of positive numbers (called labels) to the elements (vertices and/or edges) of a graph. The weight of the graph element is the sum of all labels correlated with a vertex or an edge. The labeling is irregular if the weights of edges and/or vertices are different. For a graph J we define a total labeling, such that the edge labels and vertex labels are positive integers and even integers respectively and for different edges we have different weights, then the labeling is referred as edge reflexive irregular total labeling and the edge reflexive irregularity strength of graph J is res(J). In this thesis, we give the exact values of edge reflexive irregularity strength of 𝑓 graphs generated by different families of graphs such as cycle, path and star like graphs etc.