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.
Accepted:
Published online:
Romain Boulet 1
@article{CRMATH_2008__346_13-14_711_0, author = {Romain Boulet}, title = {The centipede is determined by its {Laplacian} spectrum}, journal = {Comptes Rendus. Math\'ematique}, pages = {711--716}, publisher = {Elsevier}, volume = {346}, number = {13-14}, year = {2008}, doi = {10.1016/j.crma.2008.05.014}, language = {en}, }
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] Algebraic Graph Theory, Cambridge University Press, 1974
[2] Which graphs are determined by their spectrum?, Linear Algebra and its Applications, Volume 373 (2003), pp. 241-272
[3] Eigenvalues of graphs (L.W. Beineke; R.J. Wilson, eds.), Topics in Algebraic Graph Theory, Cambridge University Press, 2004, pp. 30-55
[4] 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] Star-like trees are determined by their Laplacian spectrum, Linear Algebra and its Applications, Volume 422 (2007), pp. 654-658
[7] Graph and some graphs related to are determined by their spectrum, Linear Algebra and its Applications, Volume 404 (2005), pp. 58-68
Cited by Sources:
Comments - Policy