Total Edge Irregularity Strength of Butterfly Networks

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 of G. In this paper we examine the butterfly network which is a well known interconnection network, and obtain its total edge irregularity strength.