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
top- [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. Zbl0940.05042
- [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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