A theorem in the theory of determinants and the number of spanning trees in a graph
A network-theoretic approach for counting the number of spanning trees of a graph is proposed. This approach is based on a theorem in the theory of determinants. Following this approach, a recurrence relation for counting Γ<sub>n</sub>, the number of spanning trees in a multigraph ladder having (<i>n</i>+1) nodes, is established. A recurrence relation is obtained connecting the sequences {<i>W</i><sub>n</sub>} and {Γ<sub>n</sub>} where <i>W</i><sub>n</sub> is the number of spanning trees in a multigraph wheel having (<i>n</i>+1) nodes. The significance of the approach is further illustrated by giving simple proofs of certain well-known results, in particular, the formula for counting the number of spanning trees in a cascade of 2-port networks.