Abstract
A recursion relation for the characteristic polynomial φ(G) of a molecular graph G is obtained, by means of which φ(G) is expressed as a linear combination of characteristic polynomials of certain edge- and vertex-deleted subgraphs of G. This result is a proper generalization of the long-known Heilbronner formula. The new recursion relation is extended to graphs with weighted edges and/or self-loops as well as to other polynomials of importance in chemical graph theory.
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