On cycle-irregularity strength of ladders and fan graphs

A simple graph G = (V(G),E(G)) admits an H-covering if every edge in E(G) belongs to at least one subgraph of G isomorphic to a given graph H. A total k-labeling φ : V(G) ∪ E(G) → {1,2,..., k} is called to be an H-irregular total k-labeling of the graph G admitting an H-covering if for every two different subgraphs H' and H" isomorphic to H there is wtφ(H') ≠ wtφ(H"), where wtφ(H)= ∑v ∈ V(H) φ(v) + ∑e ∈ E(H) φ(e). The total H-irregularity strength of a graph G, denoted by ths(G,H), is the smallest integer k such that G has an H-irregular total k-labeling. In this paper we determine the exact value of the cycle-irregularity strength of ladders and fan graphs.