Opuscula Mathematica
Opuscula Math. 42, no. 4 (2022), 561-571

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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About the authors ▼
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
About the article ▼
Communicated by Dalibor Fronček.
Received: 2021-07-27.
Revised: 2022-04-06.
Accepted: 2022-04-08.
Published online: 2022-06-30.
Cite this article as ▼
Sylwia Cichacz, Agnieszka Görlich, Andrea Semaničová-Feňovčíková, Upper bounds on distance vertex irregularity strength of some families of graphs, Opuscula Math. 42, no. 4 (2022), 561-571, https://doi.org/10.7494/OpMath.2022.42.4.561.
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