On cycle-irregularity strength of ladders and fan graphs

Abstract

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