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2020, vol. 68, iss. 1, pp. 1-7
New bounds for Laplacian energy
University of Kragujevac, Faculty of Science

emailgutman@kg.ac.rs
Abstract
Introduction/purpose: The Laplacian energy (LE) is the sum of absolute values of the terms μi-2m/n, where μi, i=1,2,…,n, are the eigenvalues of the Laplacian matrix of the graph G with n vertices and m edges. The basic results of the theory of LE are outlined, and some new obtained. Methods: Spectral theory of Laplacian matrices is applied. Results: A new class of lower bounds for LE is derived. Conclusion: The paper contributes to the Laplacian spectral theory and tp the theory of graph energies.
References
Andriantiana, E.O.D. (2016) Laplacian energy. in: Gutman I., Li X. [ed.] Graph Energies: Theory and Applications, University of Kragujevac, pp. 49-80
Cvetković, D. (1981) Teorija grafova i njene primene. Belgrade: Naučna knjiga, (in Serbian)
Grone, R., Merris, R., Sunder, V.S. (1990) The Laplacian Spectrum of a Graph. SIAM Journal on Matrix Analysis and Applications, 11(2): 218-238
Gutman, I. (2019) Oboudi-type bounds for graph energ. Mathematics Interdisciplinary Research, 4(2), pp.151-155 [online]. Available at: http://mir.kashanu.ac.ir/article_96938_35e2a0e7a15dcdd1e796325b33542469.p df. [Accessed: 30 November 2019]
Gutman, I., Furtula, B. (2019) Graph Energies: Survey, Census, Bibliography. Kragujevac: Centar SANU, Bibliography
Gutman, I., Zhou, B. (2006) Laplacian energy of a graph. Linear Algebra and Its Applications, 414(1), pp. 29-37
Harary, F. (1969) Graph Theory. Reading: Addison-Wesley
Li, X., Shi, Y., Gutman, I. (2012) Introduction. in: Graph Energy, New York, NY: Springer Science and Business Media LLC, pp.1-9
Merris, R. (1994) Laplacian matrices of graphs: A survey. Linear Algebra and its Applications, 197/198, 143-176
Oboudi, M.R. (2019) A new lower bound for the energy of graphs. Linear Algebra and its Applications, 580, pp.384-395
Potić, I., Joksimović, M., Golić, R. (2015) Changes in vegetation cover on Stara planina: Towards sustainable management of ski resorts in sensitive areas. Glasnik Srpskog geografskog društva, vol. 95, br. 2, str. 25-40
 

About

article language: English
document type: Original Scientific Paper
DOI: 10.5937/vojtehg68-24257
published in SCIndeks: 02/02/2020
peer review method: double-blind
Creative Commons License 4.0

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