New bounds on the energy of a graph

Document Type : Original paper

Authors

1 Department of Mathematics Esfahan University of Technology

2 Universidad de Antofagasta

Abstract

The energy of a graph G, denoted by Ε(G), is defined as the sum of the absolute values of all eigenvalues of G. In this paper, lower and upper bounds for energy in some of the graphs are established, in terms of graph invariants such as the number of vertices, the number of edges, and the number of closed walks.

Keywords

Main Subjects

References

[1] S. Akbari, A.H. Ghodrati, and M.A. Hosseinzadeh, Some lower bounds for the energy of graphs, Linear Algebra Appl. 591 (2020), 205–214.
2] N. Alawiah, N. Jafari Rad, A. Jahanbani, and H. Kamarulhaili, New upper bounds on the energy of a graph, Match. Commun. Math. Comput. Chem. 79 (2018), 287–301.
[3] D. Babic and I. Gutman, More lower bounds for the total π-electron energy of alternant hydrocarbons, MATCH Commun. Math. Comput. Chem. (1995), no. 32, 7–17.
[4] G. Caporossi, D. Cvetković, I. Gutman, and P. Hansen, Variable neighborhood search for extremal graphs. 2. finding graphs with extremal energy, J. Chem. Inf. Comput. Sci. 39 (1999), no. 6, 984–996.
[5] D. Cvetković, M. Doob, and H. Sachs, Spectra of Graphs Theory and Applications, Academic Press, New York, 1980.
[6] S.S. Dragomir, A survey on Cauchy-Bunyakovsky-Schwarz type discrete inequalities, J. Inequal. Pure Appl. Math. 4 (2003), no. 3, 1–142.
[7] I. Gutman and K.C. Das, Estimating the total π-electron energy, J. Serb. Chem. Soc. 78 (2013), 1925–1933.
[8] I. Gutman, S. Filipovski, and R. Jajcay, Variations on Mcclellands bound for graph energy, Discrete Math. Lett. 3 (2020), 57–60.
[9] I. Gutman and M.R. Oboudi, Bounds on graph energy, Discrete Math. Lett. 4 (2020), 1–4.
[10] I. Gutman and O.E. Polansky, Mathematical Concepts in Organic Chemistry, Springer, Berlin, 1986.
[11] I. Gutman and H. Ramane, Research on graph energies in 2019, MATCH Commun. Math. Comput. Chem. 84 (2020), no. 2, 277–292.
[12] I. Gutman, A.V. Teodorović, and L. Nedeljković, Topological properties of benzenoid systems. bounds and approximate formulae for total π-electron energy, Theor. Chim. Acta 65 (1984), no. 1, 23–31.
[13] J.H. Koolen and V. Moulton, Maximal energy graphs, Adv. Appl. Math. 26 (2001), no. 1, 47–52.
[14] X. Li, Y. Shi, and I. Gutman, Graph Energy, Springer Science & Business Media, 2012.
[15] B.J. McClelland, Properties of the latent roots of a matrix: The estimation of π-electron energies, J. Chem. Phys. 54 (1971), no. 2, 640–643.
[16] G.R. Omidi, On a signless Laplacian spectral characterization of T-shape trees, Linear Algebra Appl. 431 (2009), no. 9, 1607–1615.
[17] L. Von Collatz and U. Sinogowitz, Spektren endlicher grafen, Abh. Math. Sem. Univ. Hamburg, vol. 21, Springer, 1957, pp. 63–77.
[18] D.B. . West, Introduction to Graph Theory, Second Edition, Prentice Hall, 2001.
[19] Q. Zhou, D. Wong, and D. Sun, A lower bound for graph energy, Linear Multilinear Algebra 68 (2020), no. 8, 1624–1632.
 
Communications in Combinatorics and Optimization
Volume 7, Issue 1
June 2022
Pages 81-90

Files

Share

How to cite

Statistics