Some new upper bounds for the energy of graphs
Authors: S . B. Bozkurt Altındag, M. Matejic, I. Milovanovic, E. Milovanovic
Keywords: Energy of a graph, topological indices.
Abstract:
Let G = (V,E) be a graph of order n and size m. The energy of a graph is defined as E(G) = ΣnI=1 |λi|, where λ1 ≥ λ2 ≥ · · · ≥ λn are eigenvalues of the adjacency matrix of G. Some new upper bounds on E(G) are obtained.
References:
[1] M. BIERNACKI, H. PIDEK, C. RYLL–NARDRZESKI, Sur une inequalite entre des integrales definies, Annales Univ. Mariae Curie–Sklodowska A, 14 (1950), 1–4.
[2] B. BOROVICANIN, K. C. DAS, B. FURTULA, I. GUTMAN, Bounds for Zagreb indices, MATCH Commun. Math. Comput. Chem., 78(2017), 17–100.
[3] K. C. DAS, S. A. MOJALLAL, I. GUTMAN, Relations between degrees, conjugate degrees and graph energies, Lin. Algebra Appl. 515 (2017) 24–37.
[4] S. FAJTLOWICZ, On conjectures of Graffiti – II, Congr. Numer. 60 (1987) 189–197.
[5] I. GUTMAN, N. TRINAJSTIC , Graph theory and molecular orbitals. Total π–electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972) 535–538.
[6] I. GUTMAN, K. C. DAS, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem., 50(2004), 83–92.
[7] I. GUTMAN, The energy of a graph, Ber. Math.-Statist. Sekt. Forschungsz. Graz 103 (1978) 1–22.
[8] I. GUTMAN, E. MILOVANOVIC, I. MILOVANOVIC, Beyond the Zagreb indices, AKCE Inter. J. Graph. Comb. 17 (1) 74–85.
[9] I. GUTMAN, B. FURTULA, The total π–electron energy saga, Croat. Chem. Acta 90 (3) (2017) 359–369.
[10] I. GUTMAN, B. FURTULA, Survey of graph energies, Math. Inter. Research, 2 (2017) 85–129.
[11] I. GUTMAN, X. LI (Eds.) Energies of graphs – Theory and applicatiins, Univ. Kragujevac, Kragujevax, 2016.
[12] Y. HU, X. LI, Y. SHI, T. XU, I. GUTMAN, On molecular graphs with smallest and greatest zeroth–order general Randic index, MATCH Commun. Math. Comput. Chem. 54 (2005) 425–434.
[13] L. B. KIER, L. H. HALL, Molecular connectivity in chemistry and drug research, Academic Press, New York, 1976.
[14] H. KOBER, On the arithmetic and geometric means and on Holder’s inequality, Proc. Amer. Math. Soc. 9 (1958) 452–459.
[15] X. LI, Y. SHI, I. GUTMAN, Graph Energy, Springer, New York, 2012.
[16] X. LI, J. ZHENG, A unified approach to the extremal trees for different indices, MATCH Commun. Math. Comput. Chem. 54 (2005) 195–208
[17] A. LUPAS, A remark on the Schweitzer and Kantorevich inequalities, Univ. Beograd Publ. Elektrotehn. Fak. Ser. Mat. Fiz. 383 (1972) 13–15.
[18] A. MILICEVIC , S. NIKOLIC , On variable Zagreb indices, Croat Chem Acta 77 (2004) 97–101.
[19] P. MILOSEVIC, I. MILOVANOVIC, E. MILOVANOVIC , M. MATEJIC, Some inequalities for general zeroth–order Randi´c index, Filomat 33 (16) (2019) 5249–5258.
[20] D. S. MITRINOVIC , P. M. VASIC, Analytic Inequalities, Springer Verlag, Berlin–Heidelberg–New York, 1970.
[21] S. NIKOLIC , G. KOVACEVIC, A. MILICEVIC, N. TRINAJSTIC , The Zagreb indices 30 years after, Croat. Chem. Acta 76 (2003) 113–124.