Proof of the strong conjecture about $F$-irregular graphs in the class of graphs $\{F\}$ of diameter $2$
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908854746349568 |
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| author | Dovzhenok, Tatiana |
| author_facet | Dovzhenok, Tatiana |
| contents | Let $F$ and $G$ be simple finite undirected graphs. A graph $G$ is called $F$-irregular if any two of its distinct vertices belong to different numbers of copies of $F$ in $G$. According to the strong conjecture about $F$-irregular graphs (Dovzhenok, Filuta, Chuhai), for any connected graph $F$ of order $|F|\geqslant 3$, there exist infinitely many $F$-irregular graphs. In the present paper, the strong conjecture about $F$-irregular graphs is confirmed in the class of graphs $\{F\}$ of diameter $2$. It is proved that for every graph $F$ of diameter $2$, there exists an infinite series of $F$-irregular graphs of diameter $3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23227 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Proof of the strong conjecture about $F$-irregular graphs in the class of graphs $\{F\}$ of diameter $2$ Dovzhenok, Tatiana Combinatorics Let $F$ and $G$ be simple finite undirected graphs. A graph $G$ is called $F$-irregular if any two of its distinct vertices belong to different numbers of copies of $F$ in $G$. According to the strong conjecture about $F$-irregular graphs (Dovzhenok, Filuta, Chuhai), for any connected graph $F$ of order $|F|\geqslant 3$, there exist infinitely many $F$-irregular graphs. In the present paper, the strong conjecture about $F$-irregular graphs is confirmed in the class of graphs $\{F\}$ of diameter $2$. It is proved that for every graph $F$ of diameter $2$, there exists an infinite series of $F$-irregular graphs of diameter $3$. |
| title | Proof of the strong conjecture about $F$-irregular graphs in the class of graphs $\{F\}$ of diameter $2$ |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2602.23227 |