Geodesic
Disjoint unions of complete graphs characterized by their Laplacian spectrum
The electronic journal of linear algebra, Tome 18 (2009), pp. 773-783.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: A disjoint union of complete graphs is in general not determined by its Laplacian spectrum. It is shown in this paper that if one only considers the family of graphs without isolated vertex, then a disjoint union of complete graphs is determined by its Laplacian spectrum within this family. Moreover, it is shown that the disjoint union of two complete graphs with a and b vertices, a b > 5 3 and b > 1 is determined by its Laplacian spectrum. A counter-example is given when a b = 5 3 .
Classification : 05C50, 68R10
Keywords: graphs, Laplacian, complete graph, graph determined by its spectrum, strongly regular graph 
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     author = {Boulet, Romain},
     title = {Disjoint unions of complete graphs characterized by their {Laplacian} spectrum},
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Boulet, Romain. Disjoint unions of complete graphs characterized by their Laplacian spectrum. The electronic journal of linear algebra, Tome 18 (2009), pp. 773-783. http://geodesic.mathdoc.fr/item/ELA_2009__18__a2/