# Nonsingular unicyclic mixed graphs with at most three eigenvalues greater than two

Discussiones Mathematicae Graph Theory (2007)

- Volume: 27, Issue: 1, page 69-82
- ISSN: 2083-5892

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topShi-Cai Gong, and Yi-Zheng Fan. "Nonsingular unicyclic mixed graphs with at most three eigenvalues greater than two." Discussiones Mathematicae Graph Theory 27.1 (2007): 69-82. <http://eudml.org/doc/270617>.

@article{Shi2007,

abstract = {This paper determines all nonsingular unicyclic mixed graphs on at least nine vertices with at most three Laplacian eigenvalues greater than two.},

author = {Shi-Cai Gong, Yi-Zheng Fan},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {unicyclic graph; mixed graph; Laplacian eigenvalue; matching number; spectrum; Laplacian matrix; eigenvalues},

language = {eng},

number = {1},

pages = {69-82},

title = {Nonsingular unicyclic mixed graphs with at most three eigenvalues greater than two},

url = {http://eudml.org/doc/270617},

volume = {27},

year = {2007},

}

TY - JOUR

AU - Shi-Cai Gong

AU - Yi-Zheng Fan

TI - Nonsingular unicyclic mixed graphs with at most three eigenvalues greater than two

JO - Discussiones Mathematicae Graph Theory

PY - 2007

VL - 27

IS - 1

SP - 69

EP - 82

AB - This paper determines all nonsingular unicyclic mixed graphs on at least nine vertices with at most three Laplacian eigenvalues greater than two.

LA - eng

KW - unicyclic graph; mixed graph; Laplacian eigenvalue; matching number; spectrum; Laplacian matrix; eigenvalues

UR - http://eudml.org/doc/270617

ER -

## References

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- [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. Zbl0960.05067
- [3] Y.-Z. Fan, Largest eigenvalue of a unicyclic mixed graph, Applied Mathematics A Journal of Chinese Universities (English Series) 19 (2004) 140-148. Zbl1059.05072
- [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. Zbl1026.05076
- [6] M. Fiedler, A property of eigenvectors of nonnegative symmetric matrices and its applications to graph theory, Czechoslovak Math. J. 25 (1975) 619-633. Zbl0437.15004
- [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. Zbl0733.05060
- [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). Zbl0576.15001
- [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. Zbl1003.05073
- [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. Zbl1017.05078

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