1. On Total H-Irregularity Strength of the Disjoint Union of Graphs
- Author
-
Ashraf Faraha, López Susana Clara, Muntaner-Batle Francesc Antoni, Oshima Akito, Bača Martin, and Semaničová-Feňovčíková Andrea
- Subjects
h-covering ,h-irregular labeling ,total h-irregularity strength ,copies of graphs ,union of graphs ,05c78 ,05c70 ,Mathematics ,QA1-939 - 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.
- Published
- 2020
- Full Text
- View/download PDF