Abstract
For a simple graph G = (V, E), a vertex labeling phi : V -> {1, 2, ..., k} is called k-labeling. The weight of an edge xy in G, denoted by w(phi)(ry), is the sum of the labels of end vertices x and y. i.e w(phi)(xy) : phi(r) vertical bar phi(y). A vertex k-labeling is defined to be an edge irregular k labeling of the graph G if for every two different edges i.e. and f there is w(phi)(a) not equal w(phi)(f). The minimum k for which the graph G has an edge irregular k-labeling is called the edge irregularity strength of G. denoted by es(G).
In this paper. determine the exact value for certain families of graphs with path P-2.