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Dergiler / MATI / 2026 / Cilt: 1 Sayı: 1

On the Harmonic Energy and Estrada index of Graphs

Akbar Jahanbani(Department of Mathematics, Shahrood University of Technology, Shahrood, Iran)
Hassan Hekmatyan Raz(Department of Engineering, Yasuj Branch, Islamic Azad university, Yasuj, Iran)
Dergi
MATI
Sayfa
1–20
Yayın Tarihi
2019-01-02
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

In addition we establish upper and lower bounds for these energy and index separately also we investigate the relations between the Harmonic Estrada index and the Harmonic energy.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Let G be a graph with n vertices and di is the degree of its i-th vertex( di is the degree of vi), then the Harmonic matrix of G is the square matrix of order n whose (i; j)-entry is equal to 2 di+dj if the i-th and j-th vertex of G are adjacent, and zero otherwise.
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Temel Bulgular & Veri:The main purposes of this paper are to introduce the Harmonic Estrada index of a graph.
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Sonuç & Katkı:In addition we establish upper and lower bounds for these energy and index separately also we investigate the relations between the Harmonic Estrada index and the Harmonic energy.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Eigenvalue of graph · Energy · Harmonic Estrada index

Abstract

Let G be a graph with n vertices and di is the degree of its i-th vertex( di is the degree of vi), then the Harmonic matrix of G is the square matrix of order n whose (i; j)-entry is equal to 2 di+dj if the i-th and j-th vertex of G are adjacent, and zero otherwise. The main purposes of this paper are to introduce the Harmonic Estrada index of a graph. In addition we establish upper and lower bounds for these energy and index separately also we investigate the relations between the Harmonic Estrada index and the Harmonic energy.

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Bu Makaleye Atıf Yap

Jahanbani, A., Raz, H. H. (2019). On the Harmonic Energy and Estrada index of Graphs. MATI, Cilt: 1 Sayı: 1, 1–20. https://ajindex.com/articles/1596352

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Kaynakça (35)

  1. N. Alawiah, N. J. Rad, A. Jahanbani, H. Kamarulhaili, New Upper Boundson the Energy of a Graph, MATCH Commun. Math. Comput. Chem. 79, pp.287-301.
  2. S. Bozkurt, D. Bozkurt, Randic Energy and Randic Estrada index of a Graph,Eur. J. Pure Appl. Math, 5 (2012), 88-96.
  3. D. Cvetkovic, P. Rowlinson, S. Simic, An Introduction to the Theory of GraphSpectra, Cambridge Univ. Press, Cambridge, 2010.
  4. Z. Cvetkovski, Inequalities,Theorems, Techniques and Selected Problems,Springer-Verlag Berlin Heidelberg 2012.
  5. J. A. De la Pe~na, I. Gutman, J. Rada, Estimating the Estrada Index, Lin.Algebra Appl. 427, (2007), 70-76.
  6. H. Deng, S. Radenkovic, I. Gutman, The Estrada Index, in: D. Cvetkovic, I.Gutman (Eds.), Applications of Graph Spectra, Math. Inst., Belgrade, (2009),123-140.
  7. H. Deng, S. Balachandran, S. K. Ayyaswamy, Y. B. Venkatakrishnan, On theharmonic index and the chromatic number of a graph, preprint.
  8. H. Deng, Z. Tang, J. Zhang, On the harmonic index and the radius of a graph,preprint.
  9. H. Deng, S. Balachandran, S. K. Ayyaswamy, Y. B. Venkatakrishnan, On har-monic indices of trees, unicyclic graphs and bicyclic graphs, preprint.
  10. H. Deng, S. Balachandran, S. K.Ayyaswamy, Y. B.Venkatakrishnan, On theharmonic index and the chromatic number of a graph,Discrete Appl. Math,161(2013), 2740-2744
  11. B. Deng, Sh. Wang, I. Gutman, Resolvent Estrada index of Cycles and Paths,APPL. MATH. INFORM. AND MECH, (2016) 1, 1-10.
  12. S. S. Dragomir, On some inequalities (Romanian), Caiete Metodico Stiinti c,Faculty of Mathematics, Timisoara University, Romania. 13 1984.
  13. Z. Du, B. Zhou, On sum-connectivity index of bicyclic graphs, Bull. Malays.Math. Sci. Soc. (in press).
  14. Z. Du, B. Zhou, N. Trinajstic, Minimum general sum-connectivity index ofunicyclic graphs, J. Math. Chem. 48 (2010), 697-703.
  15. Z. Du, B. Zhou, N. Trinajstic, Minimum sum-connectivity indices of trees andunicyclic graphs of a given matching number, J. Math. Chem. 47 (2010), 842-855.
  16. E. Estrada, J. A. Rodriguez-Velazguez, Subgraph Centrality in Complex Net-works, Phys. Rev. E. 71, (2005), 056103-056103-9.
  17. A. Gungor, A. Sinan Cevik, On the Harary energy and Harary Estrada indexof a graph, MATCH Commun. Math. Comput. Chem, 64 (2010), 280-296.
  18. O. Favaron, M. Mahio, J. F. Sacle, Some eigenvalue properties in graphs (Con-jectures of Grati-II), Discrete Math. 111 (1993), 197-220.
  19. I. Gutman, M. Milun, N. Trinajstic, Comment on the paper: Properties of thelatent roots of a matrix. Estimation of -electron energies by B. J. McClelland,J. Chem. Phys. 59 (1973), 2772-2774.
  20. I. Gutman, O. E. Polansky, Mathematical Concepts in Organic Chemistry,Springer, Berlin, 1986.
  21. I. Gutman, The energy of a graph: old and new results, in: A. Betten, A.Kohnert, R. Laue and A. Wassermann (Eds.), Algebraic Combinatorics andApplications, Springer-Verlag, Berlin, (2001), 196-211.
  22. R. A. Horn, C. R. Johnson, Matrix Analysis, Cambridge Univ. Press, NewYork, 1985.
  23. S. M. Hosamani, B. B. Kulkarni, R. G. Boli, V. M. Gadag, QSPR analysis ofcertain graph theoretical matrices and their corresponding energy, Appl. Math.Nonlin. Sci 2 (2017), 131-150.
  24. A. Jahanbani, Upper bounds for the energy of graphs, MATCH Commun.Math. Comput. Chem. 79 pp. 275-286.
  25. A. Jahanbani, Lower bounds for the energy of graphs, AKCE InternationalJournal of Graphs and Combinatorics. 15 (2018) 88-96.
  26. A. Jahanbani, Some new lower bounds for energy of graphs, Applied Mathe-matics and Computation, 296 ( 2017), 233-238.
  27. X. Li, Y. Shi, I. Gutman, Graph Energy,Springer, New York, 2012.
  28. A. Lupas, Inequalities for the roots of a class of polynomials, Publ. Elektrotehn.Fak. Ser. Math. Fiz. 594 (1977) 79-85.
  29. N. Rad, A. Jahanbani, I. Gutman, Zagreb Energy and Zagreb Estrada indexof Graphs, MATCH Commun. Math. Comput. Chem, 79 (2018), 371-386.
  30. B. Zhou, Z. Du, Some lower bounds for estrada index, Iranian Journal ofMathematical Chemistry. 1, (2010), 67- 72.
  31. L. Zhong, The harmonic index for graphs, Appl. Math. Lett. 25 (2012), 561-566.
  32. B. Zhou, N. Trinajstic, On a novel connectivity index, J. Math. Chem. 46(2009), 1252-1270.
  33. B. Zhou, N. Trinajstic, On general sum-connectivity index, J. Math. Chem. 47(2010), 210-218.
  34. Z. Cvetkovski, Inequalities,Theorems, Techniques and Selected Problems,Springer-Verlag Berlin Heidelberg 2012.
  35. B. Deng, Sh. Wang, I. Gutman, Resolvent Estrada index of Cycles and Paths,APPL. MATH. INFORM. AND MECH, (2016) 1, 1-10.