发表机构
Francisk Skorina Gomel State University（弗朗西斯·斯科里纳格罗德诺国立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文指出Chartrand等人关于$K_n$-不规则图存在性的定理12缺乏完整证明，并发现$n=5$及$n\ge7$时的构造有误，质疑其作为严格证明的可靠性。
AI 中文摘要
本注记探讨了G. Chartrand等人（1987年）开创性论文“$F$-degrees in graphs”中的定理12，该定理断言对于每个$n \ge 3$，存在$K_n$-不规则图。尽管这一结果在文献中被广泛引用为既定事实，但原文缺乏完整证明。我们表明，对于$n = 5$及所有$n \ge 7$，所给出的构造并非$K_n$-不规则，这可能是由于排版错误所致。因此，将这一基础工作视为包含一般情形严格证明的引用并不完全准确。
英文摘要
This note addresses Theorem 12 in the seminal paper ``$F$-degrees in graphs'' by G. Chartrand et al. (1987), which asserts the existence of $K_n$-irregular graphs for each $n \ge 3$. Although this result is widely cited in the literature as an established fact, the original text lacks a complete proof. We show that for $n = 5$ and all $n \ge 7$, the constructions as presented are not $K_n$-irregular, presumably due to typographical errors. Consequently, referencing this foundational work as containing a rigorous proof for the general case is not entirely accurate.
