The Laplacian spectrum of some digraphs obtained from the wheel

Li Su; Hong-Hai Li; Liu-Rong Zheng

Discussiones Mathematicae Graph Theory (2012)

  • Volume: 32, Issue: 2, page 255-261
  • ISSN: 2083-5892

Abstract

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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.

How to cite

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Li Su, Hong-Hai Li, and Liu-Rong Zheng. "The Laplacian spectrum of some digraphs obtained from the wheel." Discussiones Mathematicae Graph Theory 32.2 (2012): 255-261. <http://eudml.org/doc/270893>.

@article{LiSu2012,
abstract = {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.},
author = {Li Su, Hong-Hai Li, Liu-Rong Zheng},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {digraph; Laplacian matrix; eigenvalue; wheel},
language = {eng},
number = {2},
pages = {255-261},
title = {The Laplacian spectrum of some digraphs obtained from the wheel},
url = {http://eudml.org/doc/270893},
volume = {32},
year = {2012},
}

TY - JOUR
AU - Li Su
AU - Hong-Hai Li
AU - Liu-Rong Zheng
TI - The Laplacian spectrum of some digraphs obtained from the wheel
JO - Discussiones Mathematicae Graph Theory
PY - 2012
VL - 32
IS - 2
SP - 255
EP - 261
AB - 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.
LA - eng
KW - digraph; Laplacian matrix; eigenvalue; wheel
UR - http://eudml.org/doc/270893
ER -

References

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  1. [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. Zbl1213.05107
  2. [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. Zbl1076.15012
  3. [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. Zbl0594.05046
  4. [4] J.S. Caughman and J.J.P. Veerman, Kernels of directed graph Laplacians, Electron. J. Combin. 13 (2006) R39. Zbl1097.05026
  5. [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. Zbl1017.05073
  6. [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. Zbl1163.93305
  7. [7] C. Godsil and G. Royle, Algebraic Graph Theory (Springer Verlag, 2001). 
  8. [8] A.K. Kelmans, The number of trees in a graph I, Autom. Remote Control 26 (1965) 2118-2129. 
  9. [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. Zbl0802.05053
  10. [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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