Most-vital edge of a graph with respect to spanning trees

A most-vital edge of a connected graph with respect to spanning trees is an edge whose removal most reduces the number of spanning trees. Tsen et al. (1984) proposed a solution to the problem, based on determining the adjoint of a matrix of order n (n=number of nodes of the graph). This paper presents a solution based on determining the adjoint of Ψ≡A×A^t (A=reduced incidence-matrix of the graph); the order of Ψ is (n-1). This procedure leads to a resistance-analog method to determine the vital edge of a graph with respect to the spanning trees