Abstract

Given a finite graph G it is possible to define an umbral chromatic polynomial χø(G;x) using the poset of admissible partitions of the vertices of G. We show here that an alternative construction is possible, by developing an umbral interpolation formula which generalises the classical Newton forward interpolation formula. We also explain how the new approach relates directly to the addition/contraction tree of G, and results in a simple algorithmic procedure for computing χø(G;x).

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