No abstract

Characteristic polynomials of acyclic carbon chains (Huckel trees) are treated in a systematic way. Formulas of coefficients (ar) of the polynomial are obtained in terms of connectivities that were introduced for dealing with moments in a previous paper. Based on the meaning of at, a graph-theoretical analysis is given such that ah can be expressed as a linear combination of binomial factors specified by a set of graphs containing fk edges. The numerical relationship is disclosed between each binomial factor and its specified graph. This stimulates the proposal of a novel approach for evaluating at by simply collecting the graph set of definite edges. The approach is equally applicable for the evaluation of matching polynomals of cyclic systems and extendable to the investigation of general trees.