Total edge irregularity strength of join of path and complement of a complete graph

Abstract

An edge irregular total k-labeling of a graph G is a labeling of the vertices and edges of G with labels from the set {1, 2, ..., k} in such a way that any two different edges have distinct weights. The weight of an edge uv is the sum of the label of uv and the labels of vertices u and v. The minimum k for which the graph G has an edge irregular total k-labeling is called the total edge irregularity strength of G. In this paper, we determine the exact value of the total edge irregularity strength of Pn + Km.