Total Edge Irregularity Strength of Circulant Networks and Achnia Graphs

Abstract

Given a graph G(V,E) a labeling ∂:V∪E→{1,2,...,k} is called an edge irregular total k-labeling if for every pair of distinct edges uv and xy, ∂(u)+∂(uv)+∂(v) ≠ ∂(x)+∂(xy)+∂(y). The minimum k for which G has an edge irregular total k-labeling is called the total edge irregularity strength. In this paper we consider certain graphs like achnia graphs and circulant networks and prove that they are total edge irregular.