On the total edge irregularity strength of hexagonal grid graphs.
Omar Bin Saeed Al-Mushayt, Ali Hasan Ahmad, Muhammad Kamran Siddiqui · Australas. J Comb. · 2012
An edge irregular total k-labeling of a graph G = (V,E) is a labeling φ : V ∪ E → {1, 2, . . . , k} such that the total edge-weights wt(xy) = φ(x) + φ(xy) + φ(y) are different for all pairs of distinct edges. The minimum k for which the graph G has an edge irregular total k-labeling is called the total edge irregularity strength of G. In this paper, we determined the exact values of the total edge irregularity strength of hexagonal grid graphs.