Araştırma Makalesi
BibTex RIS Kaynak Göster

On the Harmonic Energy and Estrada index of Graphs

Yıl 2019, Cilt: 1 Sayı: 1, 1 - 20, 02.01.2019

Öz

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.

Kaynakça

  • [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.
Yıl 2019, Cilt: 1 Sayı: 1, 1 - 20, 02.01.2019

Öz

Kaynakça

  • [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.
Toplam 33 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

Akbar Jahanbani

Hassan Hekmatyan Raz Bu kişi benim

Yayımlanma Tarihi 2 Ocak 2019
Kabul Tarihi 6 Temmuz 2018
Yayımlandığı Sayı Yıl 2019 Cilt: 1 Sayı: 1

Kaynak Göster

APA Jahanbani, A., & Hekmatyan Raz, H. (2019). On the Harmonic Energy and Estrada index of Graphs. MATI, 1(1), 1-20.
AMA Jahanbani A, Hekmatyan Raz H. On the Harmonic Energy and Estrada index of Graphs. Mati. Ocak 2019;1(1):1-20.
Chicago Jahanbani, Akbar, ve Hassan Hekmatyan Raz. “On the Harmonic Energy and Estrada Index of Graphs”. MATI 1, sy. 1 (Ocak 2019): 1-20.
EndNote Jahanbani A, Hekmatyan Raz H (01 Ocak 2019) On the Harmonic Energy and Estrada index of Graphs. MATI 1 1 1–20.
IEEE A. Jahanbani ve H. Hekmatyan Raz, “On the Harmonic Energy and Estrada index of Graphs”, Mati, c. 1, sy. 1, ss. 1–20, 2019.
ISNAD Jahanbani, Akbar - Hekmatyan Raz, Hassan. “On the Harmonic Energy and Estrada Index of Graphs”. MATI 1/1 (Ocak 2019), 1-20.
JAMA Jahanbani A, Hekmatyan Raz H. On the Harmonic Energy and Estrada index of Graphs. Mati. 2019;1:1–20.
MLA Jahanbani, Akbar ve Hassan Hekmatyan Raz. “On the Harmonic Energy and Estrada Index of Graphs”. MATI, c. 1, sy. 1, 2019, ss. 1-20.
Vancouver Jahanbani A, Hekmatyan Raz H. On the Harmonic Energy and Estrada index of Graphs. Mati. 2019;1(1):1-20.