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A short note on Kn-irregular graphs
Abstract
This note addresses Theorem 12 in the seminal paper ``F-degrees in graphs'' by G. Chartrand et al. (1987), which asserts the existence of Kn-irregular graphs for each n ≥ 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 ≥ 7, the constructions as presented are not Kn-irregular, presumably due to typographical errors. Consequently, referencing this foundational work as containing a rigorous proof for the general case is not entirely accurate.
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BibTeX
@misc{dovzhenok2026short,
title = {{A short note on $K_n$-irregular graphs}},
author = {Tatiana Dovzhenok},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30355},
eprint = {2609.30355},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30355},
}
RIS
TY - UNPB
TI - A short note on K_n-irregular graphs
AU - Tatiana Dovzhenok
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30355
UR - https://arxiv.org/abs/2609.30355
AB - 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 ≥ 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 ≥ 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.
ER -