On Total Edge Irregularity Strength of Certain Classes of Extended Duplicate Graphs

Abstract

Measuring irregular strength of a network mathematically is a problem of concern in communication networks.  This can be achieved by establishing edge irregular k- labeling of graph of the corresponding network.  A function from collection of vertices and edges to first k- nonnegative integers set is an edge irregular k-labeling if the labels of edges induced as sum of labels of the edges together with the labels at end vertices are all different.  The least k-value of all such edge irregular k-labeling is known as total edge irregular strength of the graph and denoted by  tes(G). Baca M  has found lower bound for all graphs.  In this paper, we find total edge irregularity strength of extended duplicate graphs of few path generated graphs.