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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1422,
author = {Yi-Zheng Fan and Song Wu},
title = {Order unicyclic graphs according to spectral radius of unoriented laplacian matrix},
journal = {Discussiones Mathematicae Graph Theory},
volume = {28},
year = {2008},
pages = {487-499},
zbl = {1173.05030},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1422}
}
Yi-Zheng Fan; Song Wu. Order unicyclic graphs according to spectral radius of unoriented laplacian matrix. Discussiones Mathematicae Graph Theory, Tome 28 (2008) pp. 487-499. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1422/
[000] [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. | Zbl 0940.05042
[001] [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. | Zbl 1113.05061
[002] [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. | Zbl 1026.05076
[003] [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. | Zbl 1059.05072
[004] [5] Y.-Z. Fan, On the least eigenvalue of a unicyclic mixed graph, Linear Multilinear Algebra 53 (2005) 97-113, doi: 10.1080/03081080410001681540. | Zbl 1062.05090
[005] [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. | Zbl 1122.05059
[006] [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.
[007] [8] M. Fiedler, Algebraic connectivity of graphs, Czechoslovak Math. J. 23 (1973) 298-305.
[008] [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. | Zbl 0817.05047
[009] [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. | Zbl 1020.05044
[010] [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. | Zbl 0802.05053
[011] [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. | Zbl 0883.05096
[012] [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. | Zbl 1149.05034
[013] [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. | Zbl 1003.05073
[014] [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. | Zbl 1017.05078