Edge irregular total labeling of certain family of graphs
Ali Hasan Ahmad, Abdus Salam, Martin Ba · 2009
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 xy their weights ϕ(x )+ ϕ(xy )+ ϕ(y )a ndϕ(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 categorical product of a cycle and a path.