Geodesic
Order unicyclic graphs according to spectral radius of unoriented laplacian matrix
Discussiones Mathematicae. Graph Theory, Tome 28 (2008) no. 3, pp. 487-499.

Voir la notice de l'article provenant de la source Library of Science

The spectral radius of a graph is defined by that of its unoriented Laplacian matrix. In this paper, we determine the unicyclic graphs respectively with the third and the fourth largest spectral radius among all unicyclic graphs of given order.
Keywords: unicyclic graph, Laplacian matrix, spectral radius 
@article{DMGT_2008_28_3_a8,
     author = {Fan, Yi-Zheng and Wu, Song},
     title = {Order unicyclic graphs according to spectral radius of unoriented laplacian matrix},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {487--499},
     publisher = {mathdoc},
     volume = {28},
     number = {3},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2008_28_3_a8/}
}
TY  - JOUR
AU  - Fan, Yi-Zheng
AU  - Wu, Song
TI  - Order unicyclic graphs according to spectral radius of unoriented laplacian matrix
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2008
SP  - 487
EP  - 499
VL  - 28
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2008_28_3_a8/
LA  - en
ID  - DMGT_2008_28_3_a8
ER  - 
%0 Journal Article
%A Fan, Yi-Zheng
%A Wu, Song
%T Order unicyclic graphs according to spectral radius of unoriented laplacian matrix
%J Discussiones Mathematicae. Graph Theory
%D 2008
%P 487-499
%V 28
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2008_28_3_a8/
%G en
%F DMGT_2008_28_3_a8
Fan, Yi-Zheng; Wu, Song. Order unicyclic graphs according to spectral radius of unoriented laplacian matrix. Discussiones Mathematicae. Graph Theory, Tome 28 (2008) no. 3, pp. 487-499. http://geodesic.mathdoc.fr/item/DMGT_2008_28_3_a8/

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

[2] D. Cvetković, P. Rowlinson and S.K. Simić, Signless Laplacians of finite graphs, Linear Algebra Appl. 423 (2007) 155-171, doi: 10.1016/j.laa.2007.01.009.

[3] Y.-Z. Fan, On spectral integral variations of mixed graph, Linear Algebra Appl. 374 (2003) 307-316, doi: 10.1016/S0024-3795(03)00575-5.

[4] Y.-Z. Fan, Largest eigenvalue of a unicyclic mixed graph, Appl. Math. J. Chinese Univ. (B) 19 (2004) 140-148, doi: 10.1007/s11766-004-0047-4.

[5] Y.-Z. Fan, On the least eigenvalue of a unicyclic mixed graph, Linear Multilinear Algebra 53 (2005) 97-113, doi: 10.1080/03081080410001681540.

[6] Y.-Z. Fan, H.-Y. Hong, S.-C. Gong and Y. Wang, Order unicyclic mixed graphs by spectral radius, Australasian J. Combin. 37 (2007) 305-316.

[7] Y.-Z. Fan, B.-S. Tam and J. Zhou, Maximizing spectral radius of unoriented Laplacian matrix over bicyclic graphs of a 798 given order, Linear and Multilinear Algebra (2007),, doi: 10.1080/03081080701306589.

[8] M. Fiedler, Algebraic connectivity of graphs, Czechoslovak Math. J. 23 (1973) 298-305.

[9] J.W. Grossman, D.M. Kulkarni and I.E. Schochetman, Algebraic Graph Theory Without Orientation, Linear Algebra Appl. 212/213 (1994) 289-307, doi: 10.1016/0024-3795(94)90407-3.

[10] Y.-P. Hou, J.-S. Li and Y.-L. Pan, On the Laplacian eigenvalues of signed graphs, Linear Multilinear Algebra 51 (2003) 21-30, doi: 10.1080/0308108031000053611.

[11] R. Merris, Laplacian matrices of graphs: a survey, Linear Algebra Appl. 197/198 (1998) 143-176, doi: 10.1016/0024-3795(94)90486-3.

[12] B. Mohar, Some applications of Laplacian eigenvalues of graphs, in: Graph Symmetry (G. Hahn and G. Sabidussi Eds (Kluwer Academic Publishers, Dordrecht, 1997) 225-275.

[13] B.-S. Tam, Y.-Z. Fan and J. Zhou, Unoriented Laplacian maximizing graphs are degree maximal, Linear Algebra Appl. (2008), doi: 10.1016/j.laa.2008.04.002.

[14] 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.

[15] X.-D. Zhang and Rong Luo, The Laplacian eigenvalues of mixed graphs, Linear Algebra Appl. 362 (2003) 109-119, doi: 10.1016/S0024-3795(02)00509-8.