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PARTITION SEIDEL ENERGY OF GRAPHS

Shashwath S Shetty|K ARATHI BHAT
장전수학회 (Jangjeon Mathematical Society)|2024.07|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제27권 제3호|pp. 469-484|DOI 10.17777/pjms.2024.27.3.006

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키워드

Seidel energyPartition matrixdivisor matrixchain graphsthreshold graphs
주제분류수학

초록

Let G be a graph with vertex set V and edge set E, and let P be a k-partition of V. In this article, we introduce the concepts of the partition Seidel matrix and partition Seidel energy, which depend on the underlying graph G and the partition of the vertex set V. We obtain an upper bound and a few lower bounds for the partition Seidel energy, and we also compute the partition Seidel energy for some families of graphs. We conclude the article by exploring the partition Seidel energy of some classes of double-nested graphs and nested split graphs.

Abstract

Let G be a graph with vertex set V and edge set E, and let P be a k-partition of V. In this article, we introduce the concepts of the partition Seidel matrix and partition Seidel energy, which depend on the underlying graph G and the partition of the vertex set V. We obtain an upper bound and a few lower bounds for the partition Seidel energy, and we also compute the partition Seidel energy for some families of graphs. We conclude the article by exploring the partition Seidel energy of some classes of double-nested graphs and nested split graphs.

참고문헌 (28)

  1. A. Alazemi, "Chain graph sequences and Laplacian spectra of chain graphs", Linear and Multilinear Algebra, 71, pp.569~585 (2022)
  2. A. Alazemi, "Eigenvalue location for chain graphs", Linear Algebra and its Applications, 505, pp.194~210 (2016)
  3. K. A. Bhat, "Forbidden values for Wiener indices of chain", threshold graphs, 2023, pp.31(1), 180~185
  4. K. A. Bhat, "Shahistha and Sudhakara G., Metric dimension and its variations of chain graphs", Proceedings of the Jangjeon Math. Soc, 24(3), pp.309~321 (2021)
  5. K. C. Das, "On energy and Laplacian energy of chain graphs", Discrete Applied Mathematics, 284, pp.391~400 (2020)
  6. P. J. Davis, "Circulant Matrices" (1979), Wiley
  7. P. D. Jacobs, "Eigenvalue location in threshold graphs", Linear Algebra and its Applications, 439, pp.2762~2773 (2013)
  8. P. D. Jacobs, "Eigenvalues and energy in threshold graphs", Linear Algebra and its Applications, 465, pp.412~425 (2015)
  9. Fedor V. Fomin, "Partial complementation of graphs", SWAT: Scandinavian Workshops on Algorithm Theory (2018)
  10. C. Godsil, "Algebraic Graph Theory, Graduate Texts in Mathematics" (2001), Springer
  11. I. Gutman, "The energy of a graph", Ber. Math. Stat. Sekt. Forschungsz. Graz, 103, pp.1~22 (1978)
  12. I. Gutman, "Laplacian energy of a graph", Linear Algebra and its Applications, 414, pp.29~37 (2006)
  13. Haemers, W.H., "Seidel switching and graph energy", MATCH Communications in mathematical and in Computer Chemistry, 68, pp.653~659 (2012)
  14. S. Hanif, "Partial chain graphs", Engineering Letters, 30(1), pp.9~16 (2022)
  15. S. Izumino, "On Ozeki’s inequality", Journal of Inequalities and Applications, 2, pp.235~253 (1998)
  16. H. Kober, "On the arithmetic and geometric means and on Holder’s inequality", Proceedings of the American Mathematical Society, 9(3), pp.452~459 (1958)
  19. B. J. McClelland, "Properties of the latent roots of a matrix: The estimation of π-electron energies", Journal of Chemical Physics, 54, pp.640~643 (1971)
  20. K. N. Prakasha, "Partition Laplacian energy of a graph", Advanced Studies in Contemporary Mathematics (Kyungshang), 27(4), pp.477~494 (2017)
  21. E. Sampathkumar, "Vertex labeled", colored graphs, matrices and signed graphs, 2014, pp.38, 113~120
  22. E. Sampathkumar, "Partition energy of a graph", Proceedings of Jangjeon Mathematical Society, 16(3), pp.335~351 (2015)
  23. E. Sampathkumar, "Partition Laplacian energy of a graph", Palestine Journal of Mathematics, 8(1), pp.272~284 (2019)
  24. S. S. Shetty, "Some properties and topological indices of k-nested graphs", IAENG International Journal of Computer Science, 50(3), pp.921~929 (2023)
  25. S. Nayak, "Partial complement energy of special graphs", IAENG International Journal of Computer Science, 49(2), pp.525~530 (2022)
  26. V. Lint J H, "Equilateral point sets in elliptic geometry", Series A : Mathematical Sciences, 69(3), pp.335~348 (1966)
  27. D. B West, "Introduction to graph theory" (2001), Prentice Hall
  28. Z. Xiong, "Eigenvalue-free interval for Seidel matrices of threshold graphs", Applied Mathematics and Computation, 427, pp.127177~ (2022)

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