Geodesic
Nonsingular unicyclic mixed graphs with at most three eigenvalues greater than two
Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 1, pp. 69-82.

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This paper determines all nonsingular unicyclic mixed graphs on at least nine vertices with at most three Laplacian eigenvalues greater than two.
Keywords: unicyclic graph, mixed graph, Laplacian eigenvalue, matching number, spectrum 
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Gong, Shi-Cai; Fan, Yi-Zheng. Nonsingular unicyclic mixed graphs with at most three eigenvalues greater than two. Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 1, pp. 69-82. http://geodesic.mathdoc.fr/item/DMGT_2007_27_1_a6/

[1] R.B. Bapat, J.W. Grossman and D.M. Kulkarni, Generalized matrix tree theorem for mixed graphs, Linear and Multilinear Algebra 46 (1999) 299-312, doi: 10.1080/03081089908818623.

[2] R.B. Bapat, J.W. Grossman and D.M. Kulkarni, Edge version of the matrix tree theorem for trees, Linear and Multilinear Algebra 47 (2000) 217-229, doi: 10.1080/03081080008818646.

[3] Y.-Z. Fan, Largest eigenvalue of a unicyclic mixed graph, Applied Mathematics A Journal of Chinese Universities (English Series) 19 (2004) 140-148.

[4] Y.-Z. Fan, On the least eigenvalue of a unicyclic mixed graph, Linear and Multilinear Algebra, accepted for publication.

[5] Y.-Z. Fan, On spectral integral variations of mixed graphs, Linear Algebra Appl. 347 (2003) 307-316, doi: 10.1016/S0024-3795(03)00575-5.

[6] M. Fiedler, A property of eigenvectors of nonnegative symmetric matrices and its applications to graph theory, Czechoslovak Math. J. 25 (1975) 619-633.

[7] R. Grone, R. Merris and V.S. Sunder, The Laplacian spectrum of a graph, SIAM J. Matrix Anal. Appl. 11 (1990) 218-238, doi: 10.1137/0611016.

[8] J.-M. Guo and S.-W. Tan, A relation between the matching number and the Laplacian spectrum of a graph, Linear Algebra Appl. 325 (2001) 71-74, doi: 10.1016/S0024-3795(00)00333-5.

[9] R.A. Horn and C.R. Johnson, Matrix analysis (Cambridge University Press, 1985).

[10] X.-D. Zhang and J.-S. Li, The Laplacian spectrum of a mixed graph, Linear Algebra Appl. 353 (2002) 11-20, doi: 10.1016/S0024-3795(01)00538-9.

[11] X.-D. Zhang and R. Luo, The Laplacian eigenvalues of a mixed graph, Linear Algebra Appl. 353 (2003) 109-119, doi: 10.1016/S0024-3795(02)00509-8.