Metraipolis › archive › dc_faddbb2c596b

On infinite families of $[P_n]$-irregular graphs — arXiv:2609.24707

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.24707
License (as archived): CC0-1.0
Archived: 2026-10-09T21:50:03.363Z
SHA-256 of the archived text: fe4b0a96a3f49673cc912d5549df259cdd1f85871511045c7d7734345bf11540
Stable URL of this page: https://metraipolis.com/documento/dc_faddbb2c596b

How to cite

On infinite families of $[P_n]$-irregular graphs — arXiv:2609.24707 — arXiv (en), https://arxiv.org/abs/2609.24707 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_faddbb2c596b (Metraipolis archive dc_faddbb2c596b, sha256 fe4b0a96a3f49673cc912d5549df259cdd1f85871511045c7d7734345bf11540)

BibTeX

@misc{dcfaddbb2c596b,
  title = {On infinite families of $[P_n]$-irregular graphs — arXiv:2609.24707},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.24707},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_faddbb2c596b; sha256 fe4b0a96a3f49673cc912d5549df259cdd1f85871511045c7d7734345bf11540},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.24707. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

This paper presents the first systematic study of $[F]$-irregular graphs, a concept that parallels classical $F$-irregularity. For a fixed graph $F$, a graph $G$ is $[F]$-irregular if the numbers of its induced subgraphs isomorphic to $F$ containing a given vertex are pairwise distinct for all vertices of $G$. We prove that there exist infinitely many $[P_n]$-irregular graphs for any path $P_n$ of order $n \ge 3$. We establish that a non-trivial $[P_3]$-irregular graph of order $k$ exists if and only if $k \ge 7$. Finally, we propose the Strong Conjecture on $[F]$-irregular graphs.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-22 in math.CO).
Categorie arXiv: Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2609.24707 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-09T21:26:41.160Z dalla pagina https://arxiv.org/catchup/math.CO/2026-09-22?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).