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NOWHERE-HARMONIC COLORINGS OF GRAPHS

Proper vertex colorings of a graph are related to its boundary map di Ə1 , also called its signed vertex-edge incidence matrix. The vertex Laplacian of a graph, L = Ə1Ət₁, a natural extension of the boundary map, leads us to introduce nowhere-harmonic colorings and analogues of the chromatic... Full description

1st Person: BECK, MATTHIAS
Additional Persons: BRAUN, BENJAMIN verfasserin
Source: in Proceedings of the American Mathematical Society Vol. 140, No. 1 (2012), p. 47-63
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Type of Publication: Article
Language: English
Published: 2012
Keywords: research-article
Online: Volltext
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Summary: Proper vertex colorings of a graph are related to its boundary map di Ə1 , also called its signed vertex-edge incidence matrix. The vertex Laplacian of a graph, L = Ə1Ət₁, 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 several examples demonstrating that nowhere-harmonic colorings are more complicated from an enumerative perspective than proper colorings.
Item Description: Copyright: © 2012 American Mathematical Scoiety
Physical Description: Online-Ressource
ISSN: 1088-6826

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