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

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

Open Access
|Apr 2025

References

  1. U. Bednarz, D. Bród, K. Piejko, and A. Włoch, (k, αn−1)-Fibonacci numbers and Pk-matchings in multigraphs, Ars Combin. 111 (2013), 354–355.
  2. U. Bednarz, D. Bród, and M. Wołowiec-Musiał, On two types of (2, k)-distance Lucas numbers, Ars Combin. 115 (2014), 467–479.
  3. U. Bednarz, A. Włoch, and M. Wołowiec-Musiał, Distance Fibonacci numbers, their interpretations and matrix generators, Comment. Math. 53 (2013), no. 1, 35–46.
  4. C. Berge, Principles of Combinatorics, Academic Press, New York-London, 1971.
  5. D. Bród, K. Piejko, and I. Włoch, Distance Fibonacci numbers, distance Lucas numbers and their applications, Ars Combin. 112 (2013), 397–409.
  6. R. Diestel, Graph Theory, Springer-Verlag, Heidelberg-New York, 2005.
  7. J. Ercolano, Matrix generator of Pell sequence, Fibonacci Quart. 17 (1979), no. 1, 71–77.
  8. E. Kiliç, The generalized order-k Fibonacci-Pell sequence by matrix methods, J. Comput. Appl. Math. 209 (2007), no. 2, 133–145.
  9. E. Kiliç, On the usual Fibonacci and generalized order-k Pell numbers, Ars Combin. 88 (2008), 33–45.
  10. E. Kiliç and D. Taşci, The generalized Binet formula, representation and sums of the generalized order-k Pell numbers, Taiwanese J. Math. 10 (2006), no. 6, 1661–1670.
  11. F. Koken and D. Bozkurt, On the Jacobsthal numbers by matrix methods, Int. J. Contemp. Math. Sci. 3 (2008), no. 13, 605–614.
  12. K. Piejko, Extremal trees with respect to numbers of (A, B, 2C)-edge colourings, J. Appl. Math. 2015, Art. ID 463650, 5 pp.
  13. K. Piejko, On k-distance Pell numbers and ((k − 1)A, (k − 1)B, kC)-edge coloured graphs, Ars Combin. 139 (2018), 197–215.
  14. K. Piejko, On the number of (A, B, 2C)-edge colourings in graphs, Ars Combin. 139 (2018), 27–41.
  15. K. Piejko and I. Włoch, On k-distance Pell numbers in 3-edge-coloured graphs, J. Appl. Math. 2014, Art. ID 428020, 6 pp.
  16. A. Szynal-Liana and I. Włoch, On distance Pell numbers and their connections with Fibonacci numbers, Ars Combin. 113A (2014), 65–75.
  17. L. Trojnar-Spelina and I. Włoch, On Pell numbers and (k1A1, k2A2, k3A3)-edge colouring in graphs, Ars Combin. 125 (2016), 183–191.
  18. I. Włoch, On generalized Pell numbers and their graph representations, Comment. Math. 48 (2008), no. 2, 169–175.
  19. I. Włoch, U. Bednarz, D. Bród, A. Włoch, and M. Wołowiec-Musiał, On a new type of distance Fibonacci numbers, Discrete Appl. Math. 161 (2013), no. 16–17, 2695–2701.
  20. A. Włoch and M. Wołowiec-Musiał, Generalized Pell numbers and some relations with Fibonacci numbers, Ars Combin. 109 (2013), 391–403.
DOI: https://doi.org/10.2478/amsil-2025-0006 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107
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
Publication frequency: 2 issues per year
Keywords:

© 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.