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For a graph G= (V, E), an edge irregular total k-labeling is a labeling of the vertices and edges of G with labels from the set 1, 2,. . . , k such that any two different edges have distinct weights. The sum of the label of edge uv and the labels of vertices u and v determines the weight of the edge uv. The smallest possible k for which the graph G has an edge irregular total k-labeling is called the total edge irregularity strength of G. We determine the exact value of the total edge irregularity strength for some cycle related graphs.
Saranya et al. (Wed,) studied this question.