图的非调和染色
Nowhere-Harmonic Colorings of Graphs
摘要：
图的真点着色与它的边界映射有关，也称为它的符号点边关联矩阵。图的顶点拉普拉斯算子是边界映射的自然扩张，它使我们引入无处调和着色和类似的色多项式以及斯坦利定理，该定理将色多项式的负评价与非循环方向联系起来。此外，我们还讨论了一些例子，证明无处调和着色更复杂，从枚举的角度比适当的着色。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
