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Journals / Hacettepe Journal of Mathematics and Statistics / 2012 / Cilt: 41 - Sayı: 4

On sum of powers of the signless Laplacian eigenvalues of graphs

Muhuo LIU
Bolian LIU
Pages
527–536
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

This note presents some properties and bounds for $S_alpha$(G) and IE(G).

📌 3 Key Takeaways

🎯
Objective & Hypothesis:For a graph G and a real number $alpha$ ( $alphaneq$ 0, 1), the graph invariant $S_alpha$(G) is the sum of the $alpha^{th}$ power of the signless Laplacian eigenvalues of G.
📊
Key Findings & Data:Let IE(G) denote the incidence energy of G, i.e., IE(G) = S1 2 (G).
💡
Conclusion & Impact:This note presents some properties and bounds for $S_alpha$(G) and IE(G).
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

For a graph G and a real number $alpha$ ( $alphaneq$ 0, 1), the graph invariant $S_alpha$(G) is the sum of the $alpha^{th}$ power of the signless Laplacian eigenvalues of G. Let IE(G) denote the incidence energy of G, i.e., IE(G) = S1 2 (G). This note presents some properties and bounds for $S_alpha$(G) and IE(G).

🔖

Cite This Article

LIU, M., LIU, B. (2022). On sum of powers of the signless Laplacian eigenvalues of graphs. Hacettepe Journal of Mathematics and Statistics, Cilt: 41 - Sayı: 4, 527–536. https://ajindex.com/articles/530470

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References (19)

  1. Akbari, S., Ghorbani, E., Koolen, J.H. and Oboudi, M.R. On sum of powers of the Lapla- cian and signless Laplacian eigenvalues of graphs, Electron. J. Combin. 17, R115, 2010
  2. Anderson, W.N. and Morley, T.D. Eigenvalues of the Laplacian of a graph, Linear Multi- linear Algebra 18, 141–145, 1985
  3. Chen, Y.Q. and Wang, L.G. Sharp bounds for the largest eigenvalue of the signless Lapla- cian of a graph, Linear Algebra Appl. 433, 908–913, 2010
  4. Cvetkovi´c, D., Rowlinson, P. and Simi´c, S.K. Signless Laplacians of finite graphs, Linear Algebra Appl. 423, 155–171, 2007
  5. Cvetkovi´c, D., Rowlinson, P. and Simi´c, S.K. Eigenvalue bounds for the signless Laplacian, Publ. Inst. Math. (Beograd), 81 (95), 11–27, 2007
  6. Cvetkovi´c, D. and Simi´c, S.K. Towards a spectral theory of graphs based on the signless Laplacian II, Linear Algebra Appl. 432, 2257–2272, 2010
  7. Gutman, I. The energy of a graph, Ber. Math Statist. Sekt. Forschungsz. Graz. 103, 1–22, 1978
  8. Gutman, I. Total n-electron energy of benzenoid hydrocarbons, Topics Curr. Chem. 162, 29–63, 1992
  9. Gutman, I. The energy of a graph: odd and new results, in: A. Betten, A. Kohnert, R. Laue, A. Wassermann (Eds.) (Algebraic Combinatorics and Applications, Springer-Verlag, Berlin, 2001), 196–211
  10. Gutman, I., Kiani, D., Mirzakhah, M. and Zhou, B. On incidence energy of a graph, Linear Algebra Appl. 431, 1223–1233, 2009
  11. Gutman, I. and Mohar, B. The quasi-Wiener and the Kirchhoff indices coincide, J. Chem. Inf. Comput. Sci. 36, 982–985, 1996
  12. Gutman, I. and Trinajsti´c, N. Graph theory and molecular orbitals, Total n-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17, 535–538, 1972
  13. Gutman, I. and Zhou, B. Laplacian energy of a graph, Linear Algebra Appl. 414, 29–37, 2006
  14. Jooyandeh, M.R., Kiani, D. and Mirzakhah, M. Incidence energy of a graph, MATCH Commun. Math. Comput. Chem. 62, 561–572, 2009
  15. Li, J. and Pan, Y. A note on the second largest eigenvalue of the Laplacian matrix of a graph, Linear Multilinear Algebra 48, 117–121, 2000
  16. Liu, J.P. and Liu, B. L. A Laplacian-energy-like invariant of a graph, MATCH Commun. Math. Comput. Chem. 59, 355–372, 2008
  17. Liu, M.H. and Liu, B. L. New sharp upper bounds for the first Zagreb index, MATCH Commun. Math. Comput. Chem. 62, 689–698, 2009
  18. Liu, M.H. and Liu, B. L. The signless Laplacian spread, Linear Algebra Appl. 432 (2-3), 505–514, 2010
  19. Li, X. L. and Zheng, J. A unified approach