Perfect bicoloring of the quintic graphs of order at most 10

  • Mohammadhadi Alaeiyan K. N. Toosi University of Technology, Seyed Khandan, Shariati Ave, 16317-14191, Tehran, Iran
  • Mehdi Alaeiyan IUST
  • Zahra Shokoohi School of Mathematics and Computer Engineering, Iran University of Science and Technology, Narmak, Tehran 16846, Iran
DOI: https://doi.org/10.5269/bspm.80127

Résumé

‎In this paper‎, ‎we investigate the problem of finding perfect bicolorings for graphs with degree five and at most 10 vertices‎. ‎A perfect bicoloring is a partition of the vertex set into two subsets such that each subset induces a regular subgraph‎. ‎We use some algebraic techniques to construct parameter matrices that encode the properties of perfect bicolorings‎. ‎We then classify all the possible parameter matrices for graphs with degree five and at most 10 vertices‎, ‎and determine which of them correspond to graphs that admit perfect bicolorings‎.

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Publiée
2025-12-21
Numéro
Vol. 43 No 3 (2025): Mathematics and Computing - Innovations and Applications (ICMSC-2025)
Rubrique
Conf. Issue: Mathematics and Computing - Innovations and Applications

Copyright (c) 2025 Boletim da Sociedade Paranaense de Matemática

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Ce travail est disponible sous la licence Creative Commons Attribution 4.0 International .

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