The centipede is determined by its Laplacian spectrum

Romain Boulet

doi:10.1016/j.crma.2008.05.014

Combinatorics

The centipede is determined by its Laplacian spectrum

Presented by: Christophe Soulé

Romain Boulet ¹

¹ Institut de mathématiques de Toulouse, Université de Toulouse et CNRS (UMR 5219), 31000 Toulouse, France

Comptes Rendus. Mathématique, Volume 346 (2008) no. 13-14, pp. 711-716

Abstract (Original language)
Résumé

A centipede is a graph obtained by appending a pendant vertex to each vertex of degree 2 of a path. In this Note we prove that the centipede is determined by its Laplacian spectrum.

Un mille-pattes est un graphe obtenu en attachant un sommet pendant à chaque sommet de degré 2 d'une chaîne. Dans cette Note nous montrons qu'un mille-pattes est déterminé par le spectre du Laplacien.

Received: 2008-02-22
Accepted: 2008-05-24
Published online: 2008-06-20

DOI: 10.1016/j.crma.2008.05.014

Author's affiliations:

Romain Boulet ¹

¹ Institut de mathématiques de Toulouse, Université de Toulouse et CNRS (UMR 5219), 31000 Toulouse, France

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     title = {The centipede is determined by its {Laplacian} spectrum},
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Romain Boulet. The centipede is determined by its Laplacian spectrum. Comptes Rendus. Mathématique, Volume 346 (2008) no. 13-14, pp. 711-716. doi: 10.1016/j.crma.2008.05.014

References
Cited by

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[2] E.R. van Dam; W.H. Haemers Which graphs are determined by their spectrum?, Linear Algebra and its Applications, Volume 373 (2003), pp. 241-272

[3] M. Doob Eigenvalues of graphs (L.W. Beineke; R.J. Wilson, eds.), Topics in Algebraic Graph Theory, Cambridge University Press, 2004, pp. 30-55

[4] B. Mohar The Laplacian spectrum of graphs, Graph Theory, Combinatorics, and Applications, Volume 2 (1991), pp. 871-898

[5] M.W. Newman, The Laplacian Spectrum of Graphs, Masters Thesis, University of Manitoba, 2000

[6] G.R. Omidi; K. Tajbakhsh Star-like trees are determined by their Laplacian spectrum, Linear Algebra and its Applications, Volume 422 (2007), pp. 654-658

[7] X. Shen; Y. Hou; Y. Zhang Graph $Z_{n}$ and some graphs related to $Z_{n}$ are determined by their spectrum, Linear Algebra and its Applications, Volume 404 (2005), pp. 58-68

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