Comptes Rendus
no. 13-14
Combinatorics
The centipede is determined by its Laplacian spectrum
[Le mille-pattes est déterminé par le spectre du Laplacien]

Présenté par : Christophe Soulé

Romain Boulet1
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.

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2008.05.014
Romain Boulet 1

1 Institut de mathématiques de Toulouse, Université de Toulouse et CNRS (UMR 5219), 31000 Toulouse, France 
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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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.05.014/

[1] N. Biggs Algebraic Graph Theory, Cambridge University Press, 1974

[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 Zn and some graphs related to Zn are determined by their spectrum, Linear Algebra and its Applications, Volume 404 (2005), pp. 58-68

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