关于$F$-不规则图的强猜想的一个完整证明

中文摘要 AI 辅助

若图$G$的所有顶点具有不同的$F$-度，则称$G$为$F$-不规则图，其中$F$-度定义为$G$中同构于给定图$F$且包含该顶点的子图数量。我们证明了关于$F$-不规则图的强猜想（Dovzhenok、Filuta和Chuhai，2024），该猜想指出：对于每个阶数至少为3的连通图$F$，存在无穷多个$F$-不规则图。这项工作从根本上推广了Chartrand等人（1987年）提出的经典存在性猜想，呈现了我们2024年2月原稿的授权英文翻译，该原稿于同年两次科学会议上全文公开报告。

英文摘要

A graph $G$ is called $F$-irregular if all its vertices have distinct $F$-degrees, defined as the number of subgraphs of $G$ isomorphic to a given graph $F$ and containing the respective vertex. We prove the Strong Conjecture about $F$-irregular graphs (Dovzhenok, Filuta, and Chuhai, 2024), which states that for every connected graph $F$ of order at least three, there exist infinitely many $F$-irregular graphs. Fundamentally generalizing the classical existence conjecture by Chartrand et al. (1987), this work presents an authorized English translation of our original February 2024 manuscript, which was publicly presented in full at two scientific conferences the same year.

发表机构

• Research Laboratory "Mathematics of Hybrid Intelligence Systems", Francisk Skorina Gomel State University（弗朗西斯·斯科里纳戈梅尔国立大学混合智能系统数学研究实验室）
• Faculty of Applied Mathematics and Computer Science, Belarusian State University（白俄罗斯国立大学应用数学与计算机科学系）

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