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arXiv · 2404.04680

On bipartite biregular large graphs

G. Araujo-Pardo·C. Dalfó·M. A. Fiol·N. López
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Abstract

A bipartite graph $G=(V,E)$ with $V=V_1\cup V_2$ is biregular if all the vertices of each stable set, $V_1$ and $V_2$, have the same degree, $r$ and $s$, 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 $d=3$ and asymptotically optimal order for given degrees $r$ and $s$. Moreover, we find some biMoore graphs, that is, bipartite biregular graphs that attain the Moore bound.

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G. Araujo-Pardo, C. Dalfó, M. A. Fiol, N. López. 2024-04-06. On bipartite biregular large graphs. https://arxiv.org/abs/2404.04680

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