The smallest eigenvalue of the signless Laplacian

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The smallest eigenvalue of the signless Laplacian

Recently the signless Laplacian matrix of graphs has been intensively investigated. While there are many results about the largest eigenvalue of the signless Laplacian, the properties of its smallest eigenvalue are less well studied. The present paper surveys the known results and presents some new ones about the smallest eigenvalue of the signless Laplacian.

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For a graph, the least signless Laplacian eigenvalue is the least eigenvalue of its signless Laplacian matrix. This paper investigates how the least signless Laplacian eigenvalue of a graph changes under some perturbations, and minimizes the least signless Laplacian eigenvalue among all the nonbipartite graphs with given matching number and edge cover number, respectively.

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The third smallest eigenvalue of the Laplacian matrix

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ژورنال

عنوان ژورنال: Linear Algebra and its Applications

سال: 2011

ISSN: 0024-3795

DOI: 10.1016/j.laa.2011.03.059