Nowhere-Harmonic Colorings of Graphs

Details Nowhere-Harmonic Colorings of Graphs Nowhere-Harmonic Colorings of Graphs

2009-07-07

arxiv.org/abs/0907.1272v3

Mathematics

Combinatorics

To appear in Proceedings of the American Mathematical Society

Scientific paper

Proper vertex colorings of a graph are related to its boundary map, also called its signed vertex-edge incidence matrix. The vertex Laplacian of a graph, a natural extension of the boundary map, leads us to introduce nowhere-harmonic colorings and analogues of the chromatic polynomial and Stanley's theorem relating negative evaluations of the chromatic polynomial to acyclic orientations. Further, we discuss some examples demonstrating that nowhere-harmonic colorings are more complicated from an enumerative perspective than proper colorings.

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