×

On the energy and Estrada index of strongly quotient graphs. (English) Zbl 1306.05141

Summary: In this paper, we consider the strongly quotient graphs and obtain some better results for the energy and Estrada index of these graphs, as well as some relations between Estrada index and the graph energy.

MSC:

05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05C78 Graph labelling (graceful graphs, bandwidth, etc.)
05C90 Applications of graph theory
92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
Full Text: DOI

References:

[1] B. Zhou, I. Gutman and T. Aleksić, A note on the Laplacian energy of graphs, MATCH Commun. Math. Comput. Chem., 60 (2008), 441–446. · Zbl 1199.05256
[2] C. Adiga and R. K. Zaferani, On coloring of strongly multiplicative and strongly quotient graphs, Adv. Stud. Cont. Math., 13(2) (2006), 171–182. · Zbl 1109.05093
[3] C. Adiga, R. K. Zaferani and M. Smitha, Strongly quotient graphs, South East Asian J. Math. & Math. Sc., 15(2) (2007), 119–127. · Zbl 1131.05061
[4] C. Adiga and R. K. Zaferani, Upper bounds for energy of a graph, Adv. Stud. Cont. Math., 16(2) (2008), 279–285. · Zbl 1188.05103
[5] D. Cvetkovic, M. Doob and H. Sachs, Spectra of Graphs-Theory and Application (Third ed. Johann Ambrosius Bart Verlag, Heidelberg, Leipzig, 1995). · Zbl 0458.05042
[6] E. Estrada, Characterization of 3D molecular structure, Chem. Phys. Lett. 319 (2000), 713–718. · doi:10.1016/S0009-2614(00)00158-5
[7] E. Estrada, Characterization of the folding degree of proteins, Bioinformatics 18 (2002), 697–704. · doi:10.1093/bioinformatics/18.5.697
[8] E. Estrada, Characterization of amino acid contribution to the folding degree of proteins, Proteins 54 (2004), 727–737. · doi:10.1002/prot.10609
[9] E. Estrada and J. A. Rodríguez-Velázguez, Subgraph centrality in complex networks, Phys. Rev., E71 (2005), 056103-1–056103-6.
[10] E. Estrada and J. A. Rodríguez-Velázguez, Spectral measures of bipartivity in complex networks, Phys. Rev., E72 (2005), 046105-1–046105-6.
[11] E. Estrada, J.A. Rodríguez-Velázguez and M. Randić, Atomic Branching in molecules, Int. J.Quantum Chem., 106 (2006), 823–832. · doi:10.1002/qua.20850
[12] I. Gutman, The energy of a graph, Ber. Math. Stat. Sckt. Forschungzentrum Graz, 103 (1978), 1–22. · Zbl 0402.05040
[13] I. Gutman Acyclic conjugated molecules, trees and their energies, J. Math. Chem., 1 (1987), 123–143.
[14] I. Gutman Total {\(\pi\)}-electron energy of benezoid hydrocarbons, Topics Curr. Chem., 162 (1992) 26–63.
[15] I. Gutman, Lower bounds for Estrada index, Publications de l’Institut Mathématique, 83(97) (2008), 1–7. · Zbl 1199.05219 · doi:10.2298/PIM0897001G
[16] J. A. De la Peña, I. Gutman and J. Rada, Estimating the Estrada index, Linear Algebra Appl., 427 (2007), 70–76. · Zbl 1184.05082 · doi:10.1016/j.laa.2007.06.020
[17] J. P. Liu and B. L. Liu, Bounds of the Estrada index of graphs, Appl. Math. J. Chinese Univ., 25(3) (2010), 325–330. · Zbl 1240.05195 · doi:10.1007/s11766-010-2237-6
[18] Y. Ginosar, I. Gutman, T. Mansour and M. Schork, Estrada index and Chbeyshev polynomials, Chemical Physics Letters, 454(4–6) (2008), 145–147. · doi:10.1016/j.cplett.2008.02.026
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.