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--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 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