Geodesic
An upper bound on the Laplacian spectral radius of the signed graphs
Discussiones Mathematicae. Graph Theory, Tome 28 (2008) no. 2, pp. 345-359

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In this paper, we established a connection between the Laplacian eigenvalues of a signed graph and those of a mixed graph, gave a new upper bound for the largest Laplacian eigenvalue of a signed graph and characterized the extremal graph whose largest Laplacian eigenvalue achieved the upper bound. In addition, an example showed that the upper bound is the best in known upper bounds for some cases.
Keywords: Laplacian matrix, signed graph, mixed graph, largest Laplacian eigenvalue, upper bound 
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     author = {Li, Hong-Hai and Li, Jiong-Sheng},
     title = {An upper bound on the {Laplacian} spectral radius of the signed graphs},
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Li, Hong-Hai; Li, Jiong-Sheng. An upper bound on the Laplacian spectral radius of the signed graphs. Discussiones Mathematicae. Graph Theory, Tome 28 (2008) no. 2, pp. 345-359. http://geodesic.mathdoc.fr/item/DMGT_2008_28_2_a9/