图与重图的弱调和标号
Weak harmonic labeling of graphs and multigraphs
摘要：
在这篇文章中，我们介绍了图的弱调和标号的概念，这是Benjamini等人最近定义的调和标号概念的推广，它允许扩展到有限图和叶子图。我们提出了各种家庭的例子，并提供了几个结构，扩展一个给定的弱调和标签到更大的图。特别是，我们使用有限的弱模型产生新的例子（强）调和标签。作为一个主要结果，我们提供了弱标号图的整数调和子集的一个特征，并使用它来计算每一个这样的图多达十个顶点。特别地，我们刻画了Benjamini等人定义的调和标号图。我们进一步将定义和主要结果推广到多重图和全标记图的情形。
英文摘要：
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.
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。
