Bounds on Nirmala energy of graphs

N. Feyza Yalçin

doi:10.2478/ausi-2022-0017

Abstract

The Nirmala matrix of a graph and its energy have recently defined. In this paper, we establish some features of the Nirmala eigenvalues. Then we propose various bounds on the Nirmala spectral radius and energy. Moreover, we derive a bound on the Nirmala energy including graph energy and maximum vertex degree.

References

[1] O. Arizmendi, O. Juarez-Romero, On bounds for the energy of graphs and di-graphs, Contributions of Mexican Mathematicians Abroad in Pure and Applied Mathematics 709 (2018) 1–19. ⇒31110.1090/conm/709/14288
Search in Google Scholar Back to article
[2] G. Arizmendi,O. Arizmendi Energy of a graph and Randic index, Linear Algebra Appl. 609 (2021) 332–338. ⇒31110.1016/j.laa.2020.09.025
Search in Google Scholar Back to article
[3] W. Dang, et al., A novel time-frequency multilayer network for multivariate time series analysis, New Journal of Physics 20 (2018) 125005. ⇒30310.1088/1367-2630/aaf51c
Search in Google Scholar Back to article
[4] K.C. Das, S. Elumalai, On energy of graphs, MATCH Commun. Math. Comput. Chem. 77 (2017) 3–8. ⇒303, 312
Search in Google Scholar Back to article
[5] K.C. Das,P. Kumar, Some new bounds on the spectral radius of graphs, Discrete Math. 281 (2004) 149–161. ⇒30610.1016/j.disc.2003.08.005
Search in Google Scholar Back to article
[6] K.C. Das,A.S.Çevik,I.N. Cangul,Y. Shang, On Sombor index, Symmetry 13 (2021) 140. ⇒30210.3390/sym13010140
Search in Google Scholar Back to article
[7] S.S. Dragomir, A survey on Cauchy-Bunyakovsky-Schwarz type discrete inequalities, J. Inequal. Pure Appl. Math. 4, 3 (2003) 1–142. ⇒312
Search in Google Scholar Back to article
[8] K. Fan, Maximum properties and inequalities for the eigenvalues of completely continuous operators, Proc. Natl. Acad. Sci. U.S.A 37, 11 (1951) 760–766. ⇒ 30910.1073/pnas.37.11.760106346416578416
Search in Google Scholar Back to article
[9] I. Gutman,E. Milovanović,I. Milovanović, Beyond the Zagreb indices, AKCE Int. J. Graphs Comb. 17, 1 (2020) 74–85. ⇒30310.1016/j.akcej.2018.05.002
Search in Google Scholar Back to article
[10] E. Musulin, Process disturbances detection via spectral graph analysis, Computer Aided Chemical Engineering 33 (2014) 1885–1890. ⇒30310.1016/B978-0-444-63455-9.50149-5
Search in Google Scholar Back to article
[11] I. Gutman, V.R. Kulli, Nirmala energy, Open Journal of Discrete Applied Mathematics 4, 2 (2021) 11-16. ⇒303, 304, 305, 308, 31310.30538/psrp-odam2021.0055
Search in Google Scholar Back to article
[12] I. Gutman, N. Trinajstić, Graph theory and molecular orbitals. Total π-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972) 535–538. ⇒302, 30310.1016/0009-2614(72)85099-1
Search in Google Scholar Back to article
[13] I. Gutman, The energy of a graph, 10. Steierm¨arkisches Mathematisches Symposium, Ber. Math.-Statist. Sekt. Forsch. Graz 103 1978, pp.1–22. ⇒303
Search in Google Scholar Back to article
[14] I. Gutman, E.A. Martins, M. Robbiano et al., Ky Fan theorem applied to Randić energy, Linear Algebra Appl. 459 (2014) 23–42. ⇒30910.1016/j.laa.2014.06.051
Search in Google Scholar Back to article
[15] R.A. Horn, C.R. Johnson, Matrix Analysis, Cambridge University Press, New York, USA, 1985. ⇒303
Search in Google Scholar Back to article
[16] A. Jahanbani, R. Khoeilar, H. Shooshtari, On the Zagreb matrix and Zagreb energy, Asian-Eur. J. Math. 15, 1 (2022) 2250019. ⇒30310.1142/S179355712250019X
Search in Google Scholar Back to article
[17] V.R. Kulli, Nirmala index, International Journal of Mathematics Trends and Technology, 67, 3 (2021) 8–12. ⇒302, 30310.14445/22315373/IJMTT-V67I3P502
Search in Google Scholar Back to article
[18] V.R. Kulli, I. Gutman, On some mathematical properties of Nirmala index, Annals of Pure and Applied Mathematics 23, 2 (2021) 93–99. ⇒30310.22457/apam.v23n2a06822
Search in Google Scholar Back to article
[19] R. Liu, W.C. Shiu, General Randić matrix and general Randić incidence matrix, Discret. Appl. Math. 186, C (2015) 168–175. ⇒30510.1016/j.dam.2015.01.029
Search in Google Scholar Back to article
[20] V. Nikiforov, The energy of graphs and matrices, J. Math. Anal. Appl. 326, 2 (2007) 1472–1475. ⇒30910.1016/j.jmaa.2006.03.072
Search in Google Scholar Back to article
[21] H. Richter, Properties of network structures, structure coefficients and benefitto-cost ratios, BioSystems 180 (2019) 88–100. ⇒30310.1016/j.biosystems.2019.03.00530914346
Search in Google Scholar Back to article
[22] H. Wiener, Structural determination of paraffin boiling points, Journal of the American Chemical Society 69, 1 (1947) 17–20. ⇒30210.1021/ja01193a00520291038
Search in Google Scholar Back to article
[23] N.F. Yalçın, On Seidel Laplacian matrix and energy of graphs, Acta Universitatis Sapientiae Informatica 14, 1 (2022) 104–118. ⇒30310.2478/ausi-2022-0007
Search in Google Scholar Back to article

Bounds on Nirmala energy of graphs

Abstract

Paradigm

My account