Comptes Rendus
no. 13-14
Combinatorics
The centipede is determined by its Laplacian spectrum
Christophe Soulé
Romain Boulet1
1Institut 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

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:
Accepted:
Published online:
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 
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
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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 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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