论文标题
在baer-lovász-tutte构造群体中的图：同构类型和同构概念
On the Baer-Lovász-Tutte construction of groups from graphs: isomorphism types and homomorphism notions
论文作者
论文摘要
令$ p $是一个奇怪的素数。从简单的无向图$ g $，到Baer的经典程序（Trans。Am。Math。Soc。，1938年，1938年），Tutte（J.Lond。Math。Soc。，1947年）和Lovász（B。Braz。Math。Soc。，1989年），与$ 2 $ 2 $ $ 2 $ $ 2 $ $ P $ p $ p $ p $ p $相关联。我们的第一个结果是表明，图形的构造尊重同构类型。也就是说，给定两个图$ g $和$ h $，$ g $和$ h $是同构图，并且仅当$ p_g $ and $ p_h $作为组为组。我们的第二个贡献是图形的新的同态概念。基于此概念，可以定义一类图形，而Baer-Lovász-Tutte构造自然会导致该图类别的函数到组类别。
Let $p$ be an odd prime. From a simple undirected graph $G$, through the classical procedures of Baer (Trans. Am. Math. Soc., 1938), Tutte (J. Lond. Math. Soc., 1947) and Lovász (B. Braz. Math. Soc., 1989), there is a $p$-group $P_G$ of class $2$ and exponent $p$ that is naturally associated with $G$. Our first result is to show that this construction of groups from graphs respects isomorphism types. That is, given two graphs $G$ and $H$, $G$ and $H$ are isomorphic as graphs if and only if $P_G$ and $P_H$ are isomorphic as groups. Our second contribution is a new homomorphism notion for graphs. Based on this notion, a category of graphs can be defined, and the Baer-Lovász-Tutte construction naturally leads to a functor from this category of graphs to the category of groups.
