论文标题
图形和多编码的较弱的谐波标记
Weak harmonic labeling of graphs and multigraphs
论文作者
论文摘要
在本文中，我们介绍了图的弱谐波标记的概念，该图的概括是Benjamini等人最近定义的谐波标记概念。这允许扩展到有限的图形和叶子图。我们介绍了各种示例家族，并提供了几种将给定的弱谐波标记扩展到较大图的构造。特别是，我们使用有限的弱模型来生成（强）谐波标记的新示例。作为主要结果，我们根据整数的谐波子集提供了弱标记的图表的表征，并使用它来计算最多十个顶点的所有此类图。特别是，我们表征了Benjamini等人定义的和谐标记的图。我们进一步将定义和主要结果扩展到多式标签和总标签的情况。
In this article we introduce the notion of weak harmonic labeling of a graph, a generalization of the concept of harmonic labeling defined recently by Benjamini et al. that allows extension to finite graphs and graphs with leaves. We present various families of examples and provide several constructions that extend a given weak harmonic labeling to larger graphs. In particular, we use finite weak models to produce new examples of (strong) harmonic labelings. As a main result, we provide a characterization of weakly labeled graphs in terms of harmonic subsets of the integers and use it to compute every such graphs of up to ten vertices. In particular, we characterize harmonically labeled graphs as defined by Benjamini et al. We further extend the definitions and main results to the case of multigraphs and total labelings.
