Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 59 min ago
PreprintarXiv licencearXiv

On infinite families of [Pn]-irregular graphs

  • Tatiana Dovzhenok
  • Ilya Lukashenko
  • Andrei Mikhalev
  • Yahor Filiuta
Open at sourcePDFDOICite

Abstract

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 [Pn]-irregular graphs for any path Pn of order n ≥ 3. We establish that a non-trivial [P3]-irregular graph of order k exists if and only if k ≥ 7. Finally, we propose the Strong Conjecture on [F]-irregular graphs.

Related

  1. Formal solution and strong asymptotic expansion of some initial value problem in two complex time variables, infinite order irregular singularities and Mahler transforms
    Alberto Lastra, Stephane Malek
    arXivPreprintCC BY-NC-ND 4.0Full textAnalysis & PDEsarXiv
  2. Irregular Hodge Bundles for Deligne--Mumford Landau--Ginzburg Families with Fixed Pole Orders
    Haoxu Wang
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  3. On the existence of F-irregular graphs for disconnected graphs F
    Tatiana Dovzhenok
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv
  4. A short note on Kn-irregular graphs
    Tatiana Dovzhenok
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv
  5. A Complete Proof of the Strong Conjecture about F-Irregular Graphs
    Tatiana Dovzhenok, Artem Filuta
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{dovzhenok2026infinite,
  title = {{On infinite families of $[P_n]$-irregular graphs}},
  author = {Tatiana Dovzhenok and Ilya Lukashenko and Andrei Mikhalev and Yahor Filiuta},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.24707},
  eprint = {2609.24707},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.24707},
}
RIS
TY  - UNPB
TI  - On infinite families of [P_n]-irregular graphs
AU  - Tatiana Dovzhenok
AU  - Ilya Lukashenko
AU  - Andrei Mikhalev
AU  - Yahor Filiuta
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.24707
UR  - https://arxiv.org/abs/2609.24707
AB  - 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 ≥ 3. We establish that a non-trivial [P_3]-irregular graph of order k exists if and only if k ≥ 7. Finally, we propose the Strong Conjecture on [F]-irregular graphs.
ER  -