Operator technique for obtaining the recursion formulas of characteristic and matching polynomials as applied to polyhex graphs

A simple and efficient method, called an operator technique, for obtaining the recurrence relation of a given counting polynomial, e.g., characteristic PG(x) or matching MG(x) polynomial, for periodic networks is proposed. By using this technique the recurrence relations of the PG(x) and MG(x) polynomials for the linear zigzag‐type and kinked polyacene graphs were obtained. For the lower members of these series of graphs, the coefficients of PG(x) and MG(x) polynomials are tabulated.

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