Counting spanning trees in the graphs of Kleitman and Golden and a generalization
The number of trees in a graph G on \(n+1\) vertices is, by the celebrated matrix tree theorem, given by the determinant of an \(n\times n\) matrix whose (i-th entry is 1 when G has an edge connecting the i-th and j-th vertices (for i and j between 1 and n) and i-th diagonal element given by minus the degree of the i-th vertex. The authors here use properties of circulant matrices to evaluate this determinant in the case in which the \((n+1)\times (n+1)\) matrix of which this is a cofactor, is a circulant.
scientific article; zbMATH DE number 3908452