Geodesic
On the Minimal Graph with a Given Number of Spanning Trees
Canadian mathematical bulletin, Tome 13 (1970) no. 4, pp. 515-517

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Let G be a finite connected graph without loops or multiple edges. A maximal tree subgraph T of G is called a spanning tree of G. Denote by k(G) the number of all trees spanning the graph G. A. Rosa formulated the following problem (private communication): Let x(≠2) be a given positive integer and denote by α(x) the smallest positive integer y having the following property: There exists a graph G on y vertices with x spanning trees. Investigate the behavior of the function α(x). 
Sedláček, J. On the Minimal Graph with a Given Number of Spanning Trees. Canadian mathematical bulletin, Tome 13 (1970) no. 4, pp. 515-517. doi: 10.4153/CMB-1970-093-0
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     title = {On the {Minimal} {Graph} with a {Given} {Number} of {Spanning} {Trees}},
     journal = {Canadian mathematical bulletin},
     pages = {515--517},
     year = {1970},
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     doi = {10.4153/CMB-1970-093-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1970-093-0/}
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