ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory 28(2) (2008) 345-359
DOI: 10.7151/dmgt.1410


Hong-Hai Li

College of Mathematic and Information Science
Jiangxi Normal University Nanchang
JiangXi, 330022 People's Republic of China

Jiong-Sheng Li

Department of Mathematics
University of Science and Technology of China
Anhui, Hefei 230026 People's Republic of China


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.

2000 Mathematics Subject Classification: 05C50, 15A18.


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Received 15 January 2008
Revised 21 April 2008
Accepted 21 April 2008