On (k1A1, k2A2, k3A3)-Edge Colourings in Graphs and Generalized Jacobsthal Numbers

Krzysztof Piejko; Lucyna Trojnar-Spelina

doi:10.2478/amsil-2025-0006

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On (k1A1, k2A2, k3A3)-Edge Colourings in Graphs and Generalized Jacobsthal Numbers

Annales Mathematicae Silesianae

Volume 39 (2025): Issue 2 (September 2025)

By: Krzysztof Piejko and Lucyna Trojnar-Spelina

Open Access

|Apr 2025

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 (k₁A₁, k₂A₂, k₃A₃)-edge colouring and quasi colouring.

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Articles in this issue

DOI: https://doi.org/10.2478/amsil-2025-0006 | Journal eISSN: 2391-4238 (formerly 0860-2107) | Journal ISSN: 0860-2107

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Language: English

Page range: 331 - 348

Submitted on: Nov 21, 2024

Accepted on: Mar 12, 2025

Published on: Apr 26, 2025

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Keywords:

Fibonacci numbers,

Jacobsthal numbers,

edge-coloured graphs,

path

MSC:

11B37,

11C20,

15B36,

05C69

Related subjects:

Mathematics,

General mathematics

© 2025 Krzysztof Piejko, Lucyna Trojnar-Spelina, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 39 (2025): Issue 2 (September 2025)