# Total edge irregularity strength of strong product of two paths

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## Resumen

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 (x1,x2) and (y1,y2) are adjacent whenever for each i ε {1,2} either Xi = yi or x1y1 ε E(Gi). An edge irregular total k-labeling φ : V ∪ E → {1,2, ...,k} of a graph G = (V, E) is a labeling of vertices and edges of G in such a way that for any different edges xy and xy their weights φ(x) + φ(xy) + φ(y) and φ(x) + φ(xy) + φ(y) are distinct. The total edge irregularity strength, tes(G), is defined as the minimum k for which G has an edge irregular total k-labeling. We have determined the exact value of the total edge irregularity strength of the strong product of two paths Pn and Pm.

Idioma original Inglés 449-459 11 Ars Combinatoria 106 Publicada - jul. 2012 Sí

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