Central indices energy of special graphs

Document Type : Original Article


Department of mathematics, statistics and computer science of Semnan university


Given a graph G with vertex set V (G) = {v1, v2, · · · , vn}. Let di be the degree of the vertex vi in G for i = 1,2, · · ·, n. We introduce the sum of degrees and the product of degrees matrices of a graph. Furthermore, we consider the central indices matrix as an Arithmetic mean matrix, Geometric mean matrix, and Harmonic mean matrix. The spectral of these matrices has been computed. In this paper, we investigate the central indices energy of some classes of graphs and several results concerning its energy have been obtained.

Graphical Abstract

Central indices energy of special graphs


[1] R. B. Bapat, Graphs and matrices, New York, Springer, 27, 2010.
[2] B. Borovicanin, E. Zogic, On Randic energy of a graph, In The 14th Serbian Mathematical Congress (14th SMAK), Kragujevac, 2018.
[3] B. Borovicanin, T.A. Lampert, On the maximum and minimum Zagreb indices of trees with a given number of vertices of maximum degree,MATCH Commun. Math. Comput. Chem. 74 (2015) 81-96.
[4] K. C. Das, I. Gutman, B. Furtula, Survey on geometric-arithmetic indices of graphs, MATCH Commun. Math. Comput. Chem. 65(3) (2011) 595-644.
[5] E. Estrada, A. Ram´ırez, Edge adjacency relationships and molecular topographic descriptors. Definition and QSAR applications, J. Chem. Inf. Comput. Sci. 36(4) (1996) 837-843.
[6] I. Gutman, The energy of a graph: old and new results, In: Algebraic combinatorics and applications, Springer, Berlin, Heidelberg, 1987.
[7] I. Gutman, B. Furtula, E. Zogic, E. Glogic, Resolvent energy of graphs, MATCH Commun. Math.
Comput. Chem. 75 (2016) 279-290.
[8] I. Gutman, B. Furtula (Eds.), Novel Molecular Structure Descriptors-Theory and Applications I ,
Univ. Kragujevac, Kragujevac, 2010.
[9] I. Gutman, S. Klavzar, B. Mohar (Eds.), Fifty years of the Wiener index, MATCH Commun. Math.
Comput. Chem. 35 (1997) 1-259.
[10] A. Jahanbani, H.H. Raz, On the harmonic energy and Estrada index of graphs, MATI. 1(1) (2019) 1-20.
[11] H. Jun, Y.M. Liu, J.K. Tian, Note on the Randic energy of graphs, Kragujev. J. Math. 42(2) (2018)
[12] S. Li, X. Li, Z. Zhu, On minimal energy and Hosoya index of unicyclic graphs, MATCH Commun.
Math. Comput. Chem. 61 (2009) 325-339.
[13] P. D. Manuel, An efficient Hosoya index algorithm and its application, IJCAET. 11(2) (2019) 196-205.
[14] O. Mekenyan, D. Bonchev, N. Trinajstic, Chemical graph theory: Modeling the thermodynamic
properties of molecules, Int. J. Quantum Chem. 18(2) (1980) 369-380.
[15] N.J. Rad, A. Jahanbani, I. Gutman, Zagreb energy and Zagreb estrada index of graphs, Match.
Commun. Math. Comput. Chem. 79 (2018) 371-386.
[16] S. Sabeti, A. B. Dehkordi, S. M. Semnani, The minimum edge covering energy of a graph. Kragujev. J. Math. 45(6) (2021) 969-975.
[17] S. K. Vaidya, K. M. Popat, Some new results on energy of graphs, MATCH Commun. Math. Comput. Chem. 77 (2017) 589-594.
[18] X. D. Zhang, Y. Liu, M. X. Han, Maximum Wiener index of trees with given degree sequence,
MATCH Commun. Math. Comput. Chem. 64 (2010) 661-682.
Volume 8, Issue 2
July 2023
Pages 105-112
  • Receive Date: 27 May 2023
  • Revise Date: 07 June 2023
  • Accept Date: 22 June 2023
  • Publish Date: 01 July 2023