title: Important mathematical structures of the topological index Z for tree graphs.
abstract: Mathematical importance of the topological index, ZG, or the so-called Hosoya index is stressed by presenting and giving supporting evidence for the proposed conjecture. That is, for a given pair of positive integers (n1<n2) which are prime with each other there exists a series of Z-trees {Gm} of the property, Z(Gm) = Z(G(m-1)) + Z(G(m-2)) (m>or=3), with Z(G1) = n1 and Z(G2) = n2.
authors.affiliation: Ochanomizu University (Emeritus), Tokyo 112-8610, Japan. hosoya@is.ocha.ac.jp
authors.forename: Haruo
authors.initials: H
authors.lastname: Hosoya