On ( <i>k</i> <sub>1</sub> <i>A</i> <sub>1</sub> , <i>k</i> <sub>2</sub> <i>A</i> <sub>2</sub> , <i>k</i> <sub>3</sub> <i>A</i> <sub>3</sub> )-Edge Colourings in Graphs and Generalized Jacobsthal Numbers
Abstract In this paper we introduce a new kind of generalized Jacobsthal numbers in a distance sense. We give the identities and matrix representations for them and their connections with the Fibonacci and the Pell numbers. We also describe the interpretations of these numbers in terms of some kind of ( k 1 A 1 , k 2 A 2 , k 3 A 3 )-edge colouring and quasi colouring.
Authors
- Krzysztof Piejko (ORCID: https://orcid.org/0000-0001-9161-3360)
- Lucyna Trojnar-Spelina (ORCID: https://orcid.org/0000-0002-9210-3757)
Institutions
- Rzeszów University of Technology (PL)
Publication Details
- Journal
- Annales Mathematicae Silesianae
- Published
- 2025-04-26
- DOI
- https://doi.org/10.2478/amsil-2025-0006
- Primary Topic
- Graph Labeling and Dimension Problems
- Type
- article
- Field-Weighted Citation Impact
- 0.00