On Bipartite Biregular Large Graphs Derived From Difference Sets
ABSTRACT A bipartite graph with is biregular if all the vertices of each stable set, and , have the same degree, and , respectively. This paper studies difference sets derived from both Abelian and non‐Abelian groups. From them, we propose some constructions of bipartite biregular graphs with diameter and asymptotically optimal order for given degrees and , meaning that asymptotically the order approaches a fixed multiple of the Moore bound. Moreover, we find some biMoore graphs, that is, bipartite biregular graphs that attain the Moore bound.
Authors
- Nacho López (ORCID: https://orcid.org/0000-0003-2534-0303)
- C. Dalfó (ORCID: https://orcid.org/0000-0002-8438-9353)
- Gabriela Araujo‐Pardo (ORCID: https://orcid.org/0000-0003-3804-1855)
- M.A. Fiol (ORCID: https://orcid.org/0000-0003-1337-4952)
Institutions
- Universitat de Lleida (ES)
- Barcelona Graduate School of Mathematics (ES)
- Universidad Nacional Autónoma de México (MX)
- Universitat Politècnica de Catalunya (ES)
Publication Details
- Journal
- Journal of Graph Theory
- Published
- 2025-05-27
- DOI
- https://doi.org/10.1002/jgt.23263
- Primary Topic
- Limits and Structures in Graph Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Ministerio de Ciencia e Innovación
- Universidad Nacional Autónoma de México
- Universitat Politècnica de Catalunya
- Agència de Gestió d'Ajuts Universitaris i de Recerca