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.

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,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 series composition of uniform theta graphs and obtain its total edge irregularity strength.We have determined the exact value of the total edge irregularity strength of this graph. We have further given an algorithm to prove the result.

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