Bipartite biregular Moore graphs

Gabriela Araujo-Pardo; Cristina Dalfó; Miguel Ángel Fiol; Nacho López

paper

Bipartite biregular Moore graphs

arXiv:2103.11443

Abstract

A bipartite graph $G = (V, E)$ with $V = V_{1} \cup V_{2}$ is biregular if all the vertices of a stable set $V_{i}$ have the same degree $r_{i}$ for $i = 1, 2$ . In this paper, we give an improved new Moore bound for an infinite family of such graphs with odd diameter. This problem was introduced in 1983 by Yebra, Fiol, and Fàbrega.\\ Besides, we propose some constructions of bipartite biregular graphs with diameter $d$ and large number of vertices $N (r_{1}, r_{2}; d)$ , together with their spectra. In some cases of diameters $d = 3$ , $4$ , and $5$ , the new graphs attaining the Moore bound are unique up to isomorphism.

19 pages, 2 figures