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arXiv · 2103.11443

Bipartite biregular Moore graphs

Gabriela Araujo-Pardo·Cristina Dalfó·Miguel Ángel Fiol·Nacho 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 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 F\`abrega.\\ 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.

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Gabriela Araujo-Pardo, Cristina Dalfó, Miguel Ángel Fiol, Nacho López. 2021-03-21. Bipartite biregular Moore graphs. https://arxiv.org/abs/2103.11443

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