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.
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