Edge irregular total labeling of certain family of graphs

Abstract

An edge irregular total k-labeling φ: V(G) ≼ E(G) → {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 x'y' their weights φ(x) + φ(xy) + φ(y) and φ(x') + φ(x'y') + 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 categorical product of a cycle and a path.