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DEDICATION This paper is dedicated to the special occasion of Gary Chartrand's 70th birthday and in recognition of his numerous contributions to graph theory. Abstract. It is an elementary exercise to show that any non-trivial simple graph has two vertices with the same degree. This is not the case for digraphs and multigraphs. We consider generating… (More)

Given a graph G (V, E) a labeling ¶: VÈE®{1, 2… k} is called an edge irregular total k-labeling if for every pair of distinct edges uv and xy, ¶(u) + ¶(uv) + ¶(v) ¹ ¶(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… (More)

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