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2020•Vojnotehnicki glasnikOpen access

New bounds for Laplacian energy

İvan Gutman

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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.

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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.

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Available 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.

Key concepts: Spectral graph theory, Laplacian matrix, Laplace operator, Eigenvalues and eigenvectors, Mathematics, Spectral theory, Graph, Class (philosophy)

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