On total edge irregularity strength of strong product of two cycles

Abstract:

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.

Año de publicación:

2017

Keywords:

• total edge irregularity strength
• Irregular assignments
• Edge irregular total labeling
• Strong product. MR (2010) subject Classification: 05C78

Fuente:

scopus