___

• [1] Büyükköse, Ş., Mutlu, N., Some bounds for the weighted energy, Sinop Uni. J. Nat. Sci., 1(2016), 62-65.
• [2] Büyükköse, Ş., Mutlu, N., Nurkahlı S.B., Some bounds for the largest eigenvalue of weighted distance matrix and weighted distance energy, Journal of Science and Arts, 2(2017), 245-256.
• [3] Consonni, V., Todeschini, R., New spectral index for molecule description, MATCH Communications in Mathematical and in Computer Chemistry, 60(2008), 3-14.
• [4] Gutman, I., Trinajsti´c, N., Graph theory and molecular orbitals. Total -electron energy of alternant hydrocarbons, Chem. Phys. Lett.,17(1972), 535-538.
• [5] Gutman, I., Ruscic, B., Trinajstic, N., Wilcox, C.F., Graph theory and molecular orbitals. XII. Acyclic polyenes, J. Chem. Phys. 62(1975), 3399-3405.
• [6] Gutman, I., The energy of a graph. Berlin Mathmatics-Statistics Forschungszentrum, 103(1978), 1-22.
• [7] Gutman, I., Polansky, O.E., Mathematical Concepts in Organic Chemistry, Springer-Verlag, Berlin, 1986.
• [8] He, C., Wang, W., Li, Y., Liu, L., Some Nordhaus-Gaddum type results of A$\alpha $ -eigenvalues of weighted graphs, Applied Mathematics and Computation, 393(2021), 1-10.
• [9] Li, X., Shi, Y., Gutman, I., Graph Energy, Springer, New York, 2012.
• [10] Li, X., Zhao, H., Trees with the first three smallest and largest generalized topological indices, MATCH Commun. Math. Comput. Chem., 50(2004), 57-62.
• [11] Li, X., Zheng, J., A unified approach to the extremal trees for different indices, MATCH Commun. Math. Comput. Chem., 54(2005), 195-208.
• [12] Ozeki, N., On the estimation of inequalities by maximum and minimum values, Journal of College Arts and Science, Chiba University, 5(1968), 199-203.(in Japanese)
• [13] P´olya, G., Szeg˝o, G., Problems and Theorems in Analysis. Vol. I: Series, Integral Calculus, Theory of Functions. Translated from the German by D. Aeppli Die Grundlehren dermathematischen Wissenschaften, Band 193. Springer-Verlag, New York-Berlin, 1972.
• [14] Rad, N.J., Jahanbani, A., Gutman, I., Zagreb energy and Zagreb estrada index of graphs, MATCH Commun. Math. Comput. Chem., 79(2018), 371-386.
• [15] Rada, J., Cruz, R., Gutman, I., Benzenoid systems with extremal vertex–degree–based topological indices, MATCH Commun. Math. Comput. Chem., 72(2014), 125-136.
• [16] Shirdel, G.H., Rezapour, H., Sayadi, A.M., The hyper–Zagreb index of graph operations, Iran. J. Math. Chem., 4 (2013), 213-220.
• [17] Shparlinski, I., On the energy of some circulant graphs, Linear Algebra and Its Applications, 414(2006), 378-382.
• [18] Tian, G., Huang, T., A note on upper bounds for the spectral radius of weighted graphs, Appl. Math. Comput., 243(2014), 392-397.
• [19] Wiener, H., Structural determination of paran boiling points, Journal of the American Chemical Society, 69(1947), 17-20.
• [20] Yu, A., Lu, M., Lower bounds on the (Laplacian) spectral radius of weighted graphs, Chinese Annals of Mathematics, Series B, 35(2014), 669-678.
• [21] Zhou, B., Trinajsti´c, N., On general sum-connectivity index, J. Math. Chem., 47(2009), 1252-1270.