On total edge irregularity strength of strong product of two cycles - Baca M.; Siddiqui M.K. (Utilitas Mathematica, 2017)
An edge irregular total k-labeling of a graph G = (V, E) is a labeling ℓ: V ∪ E → 1, 2,⋯, k such that the total edge-weights wt(ab) = ℓ(a) + ℓ(ab) + ℓ(b) are different for all pairs of distinct edges. The minimum k for which the graph G has an edge irregular total Relabeling is called the total edge irregularity strength of G. The strong product G1 G2 of graphs G1 and G2 is the graph with V(G1) × V(G2) as the vertex set, and two distinct vertices (a1,a2) and (b1,b2) are adjacent whenever for each i ϵ 1, 2 either ai = bi or aibi ϵ E(Gi). In this paper, we determine the exact value of the total edge irregularity strength of the strong product of two cycles Cn and Cm.