Geodesic
The Laplacian spectrum of some digraphs obtained from the wheel
Discussiones Mathematicae. Graph Theory, Tome 32 (2012) no. 2, pp. 255-261.

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

The problem of distinguishing, in terms of graph topology, digraphs with real and partially non-real Laplacian spectra is important for applications. Motivated by the question posed in [R. Agaev, P. Chebotarev, Which digraphs with rings structure are essentially cyclic?, Adv. in Appl. Math. 45 (2010), 232-251], in this paper we completely list the Laplacian eigenvalues of some digraphs obtained from the wheel digraph by deleting some arcs.
Keywords: digraph, Laplacian matrix, eigenvalue, wheel 
@article{DMGT_2012_32_2_a4,
     author = {Su, Li and Li, Hong-Hai and Zheng, Liu-Rong},
     title = {The {Laplacian} spectrum of some digraphs obtained from the wheel},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {255--261},
     publisher = {mathdoc},
     volume = {32},
     number = {2},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2012_32_2_a4/}
}
TY  - JOUR
AU  - Su, Li
AU  - Li, Hong-Hai
AU  - Zheng, Liu-Rong
TI  - The Laplacian spectrum of some digraphs obtained from the wheel
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2012
SP  - 255
EP  - 261
VL  - 32
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2012_32_2_a4/
LA  - en
ID  - DMGT_2012_32_2_a4
ER  - 
%0 Journal Article
%A Su, Li
%A Li, Hong-Hai
%A Zheng, Liu-Rong
%T The Laplacian spectrum of some digraphs obtained from the wheel
%J Discussiones Mathematicae. Graph Theory
%D 2012
%P 255-261
%V 32
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2012_32_2_a4/
%G en
%F DMGT_2012_32_2_a4
Su, Li; Li, Hong-Hai; Zheng, Liu-Rong. The Laplacian spectrum of some digraphs obtained from the wheel. Discussiones Mathematicae. Graph Theory, Tome 32 (2012) no. 2, pp. 255-261. http://geodesic.mathdoc.fr/item/DMGT_2012_32_2_a4/

[1] R. Agaev and P. Chebotarev, Which digraphs with rings structure are essentially cyclic?, Adv. in Appl. Math. 45 (2010) 232-251, doi: 10.1016/j.aam.2010.01.005.

[2] R. Agaev and P. Chebotarev, On the spectra of nonsymmetric Laplacian matrices, Linear Algebra Appl. 399 (2005) 157-168, doi: 10.1016/j.laa.2004.09.003.

[3] W.N. Anderson and T.D. Morley, Eigenvalues of the Laplacian of a graph, Linear Multilinear Algebra 18 (1985) 141-145, doi: 10.1080/03081088508817681.

[4] J.S. Caughman and J.J.P. Veerman, Kernels of directed graph Laplacians, Electron. J. Combin. 13 (2006) R39.

[5] P. Chebotarev and R. Agaev, Forest matrices around the Laplacian matrix, Linear Algebra Appl. 356 (2002) 253-274, doi: 10.1016/S0024-3795(02)00388-9.

[6] P. Chebotarev and R. Agaev, Coordination in multiagent systems and Laplacian spectra of digraphs, Autom. Remote Control 70 (2009) 469-483, doi: 10.1134/S0005117909030126.

[7] C. Godsil and G. Royle, Algebraic Graph Theory (Springer Verlag, 2001).

[8] A.K. Kelmans, The number of trees in a graph I, Autom. Remote Control 26 (1965) 2118-2129.

[9] R. Merris, Laplacian matrices of graphs: A survey, Linear Algebra Appl. 197/198 (1994) 143-176, doi: 10.1016/0024-3795(94)90486-3.

[10] R. Olfati-Saber, J.A. Fax and R.M. Murray, Consensus and cooperation in networked multi-agent systems, Proc. IEEE 95 (2007) 215-233, doi: 10.1109/JPROC.2006.887293.