On total h-irregularity strength of the disjoint union of graphs

Faraha Ashraf, Susana Clara López, Francesc Antoni Muntaner-Batle, Akito Oshima, Martin Bača, Andrea Semaničová-Feňovčíková

Producción científica: Contribución a una revistaArtículorevisión exhaustiva

1 Cita (Scopus)


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. In this paper, we estimate lower and upper bounds on the total H-irregularity strength for the disjoint union of multiple copies of a graph and the disjoint union of two non-isomorphic graphs. We also prove the sharpness of the upper bounds.

Idioma originalInglés
Páginas (desde-hasta)181-194
Número de páginas14
PublicaciónDiscussiones Mathematicae - Graph Theory
EstadoPublicada - 1 feb. 2020
Publicado de forma externa


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