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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.
Słowa kluczowe
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
255-261
Opis fizyczny
Daty
wydano
2012
otrzymano
2011-02-10
poprawiono
2011-05-10
zaakceptowano
2011-05-10
Twórcy
autor
- College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, 330022, P.R. China
autor
- College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, 330022, P.R. China
autor
- College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, 330022, P.R. China
Bibliografia
- [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.
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1612