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

• Autorzy: Shi-Cai Gong , Yi-Zheng Fan
• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

unicyclic graph; mixed graph; Laplacian eigenvalue; matching number; spectrum

Kategorie tematyczne

• 05C50: Graphs and linear algebra (matrices, eigenvalues, etc.)
• 15A18: Eigenvalues, singular values, and eigenvectors

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2007
• Tom: 27
• Numer: 1
• Strony: 69-82

Daty

wydano

2007

otrzymano

2005-09-23

poprawiono

2006-11-29

Twórcy

autor

Shi-Cai Gong

• School of Mathematics and Computational Science, Anhui University, Hefei, Anhui 230039, P.R. China
• Department of Mathematics and Physics, Anhui University of Science and Technology, Anhui, Huainan 232001

autor

Yi-Zheng Fan

• School of Mathematics and Computational Science, Anhui University, Hefei, Anhui 230039, P.R. China

Bibliografia

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• [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.

Identyfikatory

DOI

10.7151/dmgt.1345