关于细谷的休眠和萌芽
On Hosoya's dormants and sprouts
摘要：
在最近的一系列论文中，细谷引起了人们对使用聚结构造共谱图的一个特殊方面的注意：共谱图可以通过将有根图的多个副本以不同的方式附加到底层图的顶点子集上来构造。我们的主要重点是解决细谷的论文中提出的关于这一建设的期望和问题。我们给出了这类多重聚结的特征多项式的一个显式公式，由此得到了它们共谱的一个充要条件。我们列举了这样的同谱多聚结的几个家庭的基础图形，并显示了无限的同谱多聚结的路径作为基础图形，这被认为是罕见的细谷。
英文摘要：
In a recent series of papers, Hosoya drew the attention to a particular aspect of constructing cospectral graphs by using coalescences: that cospectral graphs can be constructed by attaching multiple copies of a rooted graph in different ways to subsets of vertices of an underlying graph. Our principal focus is to address the expectations and questions raised in Hosoya's papers with regards to this construction. We give an explicit formula for the characteristic polynomial of such multiple coalescences, from which we obtain a necessary and sufficient condition for their cospectrality. We enumerate such cospectral multiple coalescences for a few families of underlying graphs, and show the infinitude of cospectral multiple coalescences having paths as underlying graphs, which were deemed rare by Hosoya.
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。
