Let G be a graph with vertex set V(G) and edge set E(G). For any two vertices x and y in V(G), the distance between x and y, denoted by d(x,y), is the length of the shortest path connecting x and y. The degree of a vertex v in G is the number of neighbors of v in G. Numbers reflecting certain structural features of organic molecules that are obtained from the molecular graph are usually called ...

The Hosoya polynomial triangle is a triangular arrangement of polynomials where each entry is a product of two polynomials. The geometry of this triangle is a good 1 tool to study the algebraic properties of polynomial products. In particular, we find closed formulas for the alternating sum of products of polynomials such as Fibonacci polynomials, Chebyshev polynomials, Morgan-Voyce polynomials...

Based on the total π-electron energies Eπs of Hückel Molecular Orbital (HMO) method for all the possible isomers of conjugated acyclic polyenes (C₂nH₂n+2) up to n = 7, the structure-stability relation of the possible isomers was analyzed. It was shown that the mean length of conjugation L can roughly predict the ordering of stability among isomers, while the Z-index, or Hosoya-index, can almost...