Two-cacti with minimum number of spanning trees
A cactus is an undirected graph which contains at least one circuit and in which any two circuits have at most one vertex in common. A two-cactus is a cactus which contains exactly two circuits. The number of isomorphism classes of spanning trees of two-cacti is studied. Four constructions of two-cacti are described. It is proved that there are exactly three isomorphism classes of spanning trees of a two-cactus \(G\) if and only if \(G\) is obtained by one of the described constructions.
scientific article; zbMATH DE number 500622