chapter  Chapter 10
8 Pages

Counting Polynomials

WithLorentz Jäntschi, Sorana D. Bolboacă

A topological description of a molecule requires the storing of the adjacencies between the atoms and the identities. By disregarding the bond and atom types, if this problem is simplified at maximum, then adjacencies are simply stored with 0 and 1 in the vertex adjacency matrix ([Ad]) and the identities are stored with 0 and 1 into the identity matrix. The counting polynomial (CoP) is a construction of a polynomial in which the values in the originating matrix are expressed in a polynomial function in which the coefficient of each monomial count the occurrences of the value used to express the degree of the monomial. A counting polynomial is a description of a graph property P(G), in terms of a sequence of numbers, so that the exponents express the extent of its partitions while the coefficients are related to the frequency of the occurrence of partitions.