Geodesic
A new Spectral Method for Determining the Number of Spanning Trees
Publications de l'Institut Mathématique, _N_S_29 (1981) no. 43, p. 49

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

As is known, the number of spanning tress of a regular graph can be determined by the graph spectrum. In this paper we describe a new variant of the spectral method for determining the number of spanning trees, which enables to solve the problem for a class of non-regular graphs. 
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     author = {Drago\v{s} Cvetkovi\'c and Ivan Gutman},
     title = {A new {Spectral} {Method} for {Determining} the {Number} of {Spanning} {Trees}},
     journal = {Publications de l'Institut Math\'ematique},
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Dragoš Cvetković; Ivan Gutman. A new Spectral Method for Determining the Number of Spanning Trees. Publications de l'Institut Mathématique, _N_S_29 (1981) no. 43, p. 49 . http://geodesic.mathdoc.fr/item/PIM_1981_N_S_29_43_a6/