1. On total H-irregularity strength of the disjoint union of graphs
- Author
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Andrea Semaničová-Feňovčíková, Faraha Ashraf, Akito Oshima, Francesc-Antoni Muntaner-Batle, Martin Bača, and S. C. López
- Subjects
copies of graphs ,05c70 ,Applied Mathematics ,h-irregular labeling ,union of graphs ,Combinatorics ,Disjoint union (topology) ,QA1-939 ,h-covering ,Discrete Mathematics and Combinatorics ,05c78 ,total h-irregularity strength ,Mathematics - 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