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

• Main Authors: Ashraf Faraha, López Susana Clara, Muntaner-Batle Francesc Antoni, Oshima Akito, Bača Martin, Semaničová-Feňovčíková Andrea
• Format: Article
• Language: English
• Published: Sciendo 2020-02-01
• Series: Discussiones Mathematicae Graph Theory
• Subjects: h-covering; h-irregular labeling; total h-irregularity strength; copies of graphs; union of graphs; 05c78; 05c70
• Online Access: https://doi.org/10.7151/dmgt.2118
• ISSN: 2083-5892

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.