Counting Polynomials in Tori T(4,4)S[c,n]

A counting polynomial P(x) 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 number of partitions of a given extent. Basic definitions and some properties are given for two classes of polynomials, called here polynomials of vertex proximity and edge proximity, respectively. Formulas to calculate these polynomials in T(4,4)[c,n] tori are derived by a cutting procedure.