Opuscula Math. 42, no. 4 (2022), 561-571
https://doi.org/10.7494/OpMath.2022.42.4.561
Opuscula Mathematica
Upper bounds on distance vertex irregularity strength of some families of graphs
Sylwia Cichacz
Agnieszka Görlich
Andrea Semaničová-Feňovčíková
Abstract. For a graph \(G\) its distance vertex irregularity strength is the smallest integer \(k\) for which one can find a labeling \(f: V(G)\to \{1, 2, \dots, k\}\) such that \[ \sum_{x\in N(v)}f(x)\neq \sum_{x\in N(u)}f(x)\] for all vertices \(u,v\) of \(G\), where \(N(v)\) is the open neighborhood of \(v\). In this paper we present some upper bounds on distance vertex irregularity strength of general graphs. Moreover, we give upper bounds on distance vertex irregularity strength of hypercubes and trees.
Keywords: distance vertex irregularity strength of a graph, hypercube, tree.
Mathematics Subject Classification: 05C65, 05C78.
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- Sylwia Cichacz
https://orcid.org/0000-0002-7738-0924- AGH University of Science and Technology, Faculty of Applied Mathematics, al. A. Mickiewicza 30, 30-059 Kraków, Poland
- Agnieszka Görlich (corresponding author)
- https://orcid.org/0000-0002-7198-0531
- AGH University of Science and Technology, Faculty of Applied Mathematics, al. A. Mickiewicza 30, 30-059 Kraków, Poland
- Andrea Semaničová-Feňovčíková
- https://orcid.org/0000-0002-8432-9836
- Technical University, Department of Applied Mathematics and Informatics, Košice, Slovakia
- Communicated by Dalibor Fronček.
- Received: 2021-07-27.
- Revised: 2022-04-06.
- Accepted: 2022-04-08.
- Published online: 2022-06-30.
