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 
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/
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     title = {A new {Spectral} {Method} for {Determining} the {Number} of {Spanning} {Trees}},
     journal = {Publications de l'Institut Math\'ematique},
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     year = {1981},
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     number = {43},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1981_N_S_29_43_a6/}
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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.