The author continues the investigation of \textit{H. Shank} in the papers ''Graph property recognition machines'' published in Math. Systems Theory 5 (1971), and ''The theory of left-right paths'' [Comb. Math. III, Proc. 3rd Australian Conf., St. Lucia 1974, Lect. Notes Math. 452, 42-54 (1975; Zbl 0307.05120)]. Let G be a connected multigraph. Furthermore let \((A,+\), 0) be any Abelian group. Then for any non-negative integer k A(k) denote the subgroup \(A(k)=\{a\in A| ka=0\}\) of A. At first the author shows that the spanning tree number t of G has a unique factorization \(t=t_ 1t_ 2...t_ m\) with certain properties such that for every Abelian group A the group B(A) of bicycles over A isomorphic to the direct product \(A(t_ 1)\times A(t_ 2)\times...\times A(t_ m)\). Furthermore he obtains a formula for the factors in a (principal) factorization. Finally, he proves that a planar graph and its dual graph have the same spanning tree number with the same (principal) factorization. Defining the notion ''a k-bicycle is reducible'', he shows that there exists a relationship between the number of irreducible k- bicycles and the spanning tree number t.