论文标题
路径界阿贝尔群体
Path-cordial abelian groups
论文作者
论文摘要
通过任何Abelian Group $ a $元素对图的顶点的标签，可以通过求和其端点的标签来引起边缘的标签。霍维（Hovey）将图形$ g $定义为$ a $ cordial，如果它具有这样的标签，从而在技术意义上都将顶点标签和边缘标签都均匀地分布在$ a $上。他认为，所有环环$ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $的猜想尽管有很大的关注。奇怪的是，几乎没有研究Hovey的猜想可能会超越循环群体的范围。 我们通过分析较大的有限的Abelian Groups $ a $来启动这项研究，从而使所有路径图都是$ a-cordial。我们猜想了此类群体的完整表征，并为各个无限的群体以及所有小阶组的群体建立了这种猜想。
A labeling of the vertices of a graph by elements of any abelian group $A$ induces a labeling of the edges by summing the labels of their endpoints. Hovey defined the graph $G$ to be $A$-cordial if it has such a labeling where the vertex labels and the edge labels are both evenly-distributed over $A$ in a technical sense. His conjecture that all trees $T$ are $A$-cordial for all cyclic groups $A$ remains wide open, despite significant attention. Curiously, there has been very little study of whether Hovey's conjecture might extend beyond the class of cyclic groups. We initiate this study by analyzing the larger class of finite abelian groups $A$ such that all path graphs are $A$-cordial. We conjecture a complete characterization of such groups, and establish this conjecture for various infinite families of groups as well as for all groups of small order.
