On Total H-Irregularity Strength of the Disjoint Union of Graphs

Abstract

A simple graph G admits an H-covering if every edge in E(G) belongs to at least to one subgraph of G isomorphic to a given graph H. For the subgraph H ⊆ G under a total k-labeling we define the associated H-weight as the sum of labels of all vertices and edges belonging to H. The total k-labeling is called the H-irregular total k-labeling of a graph G admitting an H-covering if all subgraphs of G isomorphic to H have distinct weights. The total H-irregularity strength of a graph G is the smallest integer k such that G has an H-irregular total k-labeling.

Keywords

• h-covering
• h-irregular labeling
• total h-irregularity strength
• copies of graphs
• union of graphs
• 05c78
• 05c70