The Laplacian spectrum of some digraphs obtained from the wheel

• Autorzy: Li Su , Hong-Hai Li , Liu-Rong Zheng
• Języki publikacji: EN

Abstrakty

EN

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

EN

digraph; Laplacian matrix; eigenvalue; wheel

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: 2012
• Tom: 32
• Numer: 2
• Strony: 255-261

Daty

wydano

2012

otrzymano

2011-02-10

poprawiono

2011-05-10

zaakceptowano

2011-05-10

Twórcy

autor

Li Su

• College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, 330022, P.R. China

autor

Hong-Hai Li

• College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, 330022, P.R. China

autor

Liu-Rong Zheng

• 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.

Identyfikatory

DOI

10.7151/dmgt.1612