English

New Constructions of Distance-Biregular Graphs

Combinatorics 2026-05-01 v3

Abstract

We construct a new family of distance-biregular graphs related to hyperovals and a new sporadic example of a distance-biregular graph related to Mathon's perp system. The infinite family can be explained using 2-\bipartB\bipartB-homogeneity, while the sporadic example belongs to a generalization of a construction by Delorme. Additionally, we establish a new non-existence condition for distance-biregular graphs which, for instance, rules out the existence of a distance-biregular graph on 225+60225+60 vertices.

Keywords

Cite

@article{arxiv.2504.21488,
  title  = {New Constructions of Distance-Biregular Graphs},
  author = {Blas Fernández and Ferdinand Ihringer and Sabrina Lato and Akihiro Munemasa},
  journal= {arXiv preprint arXiv:2504.21488},
  year   = {2026}
}

Comments

30 pages, a minor typo corrected