Abstract
A total edge irregular [Formula: see text]-labeling of a graph [Formula: see text], [Formula: see text] is a labeling of vertices and edges of [Formula: see text] in such a way that the weights of all edges are distinct. A total edge irregularity strength of graph [Formula: see text], denoted by [Formula: see text] is defined as the minimum [Formula: see text] for which a graph [Formula: see text] has a totally irregular total [Formula: see text]-labeling. In this paper, we define [Formula: see text]-total edge irregularity labeling and provide the irregularity strength for some well-known families of graphs.
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