New bounds for spectral radius and the geometric-arithmetic energy of graphs

Hajar Shoohstari; Murat  Cancan

doi:10.5269/bspm.66145

Hajar Shoohstari Azarbaijan Shahid Madani University
Murat Cancan

Abstract

In this paper, new bounds on the GA-energy of graphs are established. Moreover, we show the our bounds are stronger than some previously known lower and upper bounds in the literature.

Downloads

Download data is not yet available.

References

M. Biernacki, H. Pidek, C. Ryll-Nardzewski, Sur une inegalite entre des integrales definies, Univ. Marie Curie-Sklodowska A4. (1950) 1–4.

V. Cirtoaje, The best lower bound depended on two fixed variables for Jensen’s inequality with ordered variables, J. Inequal. Appl. 2010 (2010), 1–12.

I. Gutman, The energy of a graph: old and new results, in: A. Betten, A. Kohnert, R. Laue and A. Wassermann (Eds.), Algebraic Combinatorics and Applications, Springer-Verlag, Berlin, (2001), 196-211.

A. Jahanbani, Some new lower bounds for energy of graphs, Appl. Math. Comput. 296 ( 2017), 233-238.

A. Jahanbani, J. R. Zambrano, Koolen-Moulton-type upper bounds on the energy of a graph, MATCH Commun. Math. Comput. Chem. 83 (2020), 497–518.

A. Jahanbani, R. Khoeilar, H. Shooshtari, On the Zagreb matrix and Zagreb energy, Asian-Eur. J. Math. (2021), https://doi.org/10.1142/S179355712250019X.

H. Kober, On the arithmetic and geometric means and the Holder inequality, Proc. Am. Math. Soc. 59(1958), 452–459.

A. Lupas, Inequalities for the roots of a class of polynomials, Publikacije Elektrotehnickog fakulteta. Serija Matematika i fizika 577/598 (1977), 79–85.

D. S. Mitrinovic, J. E. Pecaric, A. M. Fink, Classical and New Inequalities in Analysis, Kluwer, Dordecht, 1993.

D. S. Mitrinovic, P. M. Vasic, Analytic Inequalities, Springer, Berlin, 1970.

J. M. Rodrıguez, J. M. Sigarreta, Spectral properties of geometric-arithmetic index, Applied Mathematics and Computation. 277 (2016), 142–153.

J. M. Rodrıguez, J. M. Sigarreta, Spectral study of the geometric-arithmetic index, MATCH Commun. Math. Comput. Chem. 74 (2015), 121–135.

P. Schweitzer, An inequality about the arithmetic mean, Math. Phys. Lapok (Budapest). 23 (1914) 257–261.

D. Vukicevic, B. Furtula, Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges, J. Math. Chem. 46(2009), 1369–1376.

H. Shooshtary, J. Rodrıguez, New bounds on the energy of a graph, Commun. Comb. Optim. 7 (2022) 81–90.

B. Zhou, I. Gutman, T. Aleksic, A note on the Laplacian energy of graphs, MATCH Commun. Math. Comput. Chem. 60 (2008), 441–446.

B. Zhou, I. Gutman, J. Antonio de la Pena, J. Rada, L. Mendoza, On spectral moments and energy of graphs, MATCH Commun. Math. Comput. Chem. 57 (2007), 183–191.