Connectivity, toughness, spanning trees of bounded degree, and the spectrum of regular graphs
Czechoslovak Mathematical Journal, Tome 66 (2016) no. 3, pp. 913-924.

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The eigenvalues of graphs are related to many of its combinatorial properties. In his fundamental work, Fiedler showed the close connections between the Laplacian eigenvalues and eigenvectors of a graph and its vertex-connectivity and edge-connectivity. \endgraf We present some new results describing the connections between the spectrum of a regular graph and other combinatorial parameters such as its generalized connectivity, toughness, and the existence of spanning trees with bounded degree.
DOI : 10.1007/s10587-016-0300-z
Classification : 05C05, 05C40, 05C42, 05C50, 05E99, 15A18
Mots-clés : spectral graph theory; eigenvalue; connectivity; toughness; spanning $k$-tree 
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Cioabă, Sebastian M.; Gu, Xiaofeng. Connectivity, toughness, spanning trees of bounded degree, and the spectrum of regular graphs. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 3, pp. 913-924. doi : 10.1007/s10587-016-0300-z. https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-016-0300-z/

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