Bipartite biregular Moore graphs

2021/03/21 by Gabriela Araujo-Pardo, Cristina Dalfó, Araujo-Pardo, Gabriela +5
Mathematics · #05C50 #51E12 #5C35 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C50 #msc:51E12 #msc:5C35

paper · pdf · doi:10.48550/arxiv.2103.11443

19 pages, 2 figures

arxiv created 2021/03/21 · arxiv updated 2021/03/23

Abstract

A bipartite graph G=(V,E) with V=V₁∪ V₂ 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(r₁,r₂;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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