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. Ts
en et al (1984) proposed a solution to the problem, based on determini
ng the adjoint of a matrix of order n (n = number of nodes of the grap
h). This paper presents a solution based on determining the adjoint of
Psi = A x A(t) (A = reduced incidence-matrix of the graph); the order
of Psi is (n - 1). This procedure leads to a resistance-analog method
to determine the vital edge of a graph with respect to the spanning t
rees.