# 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

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