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arXiv · 1508.00386

New Bounds for the Sum of Powers of Normalized Laplacian Eigenvalues of Graphs

Gian Paolo Clemente·Alessandra Cornaro
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Abstract

For a simple and connected graph, a new graph invariant $s_{\alpha}^{*}(G)$, defined as the sum of powers of the eigenvalues of the normalized Laplacian matrix, has been introduced by Bozkurt and Bozkurt in [7]. Lower and upper bounds have been proposed by the authors. In this paper, we localize the eigenvalues of the normalized Laplacian matrix by adapting a theoretical method, proposed in Bianchi and Torriero ([5]), based on majorization techniques. Through this approach we derive upper and lower bounds of $s_{\alpha}^{*}(G)$. Some numerical examples show how sharper results can be obtained with respect to those existing in literature.

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Gian Paolo Clemente, Alessandra Cornaro. 2015-08-03. New Bounds for the Sum of Powers of Normalized Laplacian Eigenvalues of Graphs. https://arxiv.org/abs/1508.00386

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