Resumen de On bipartite biregular Moore graphs

Gabriela Araujo-Pardo, Cristina Dalfó Simó, Miguel Ángel Fiol Mora, Nacho López

• The degree/diameter problem for graphs consists in finding the largest order of a graphwith prescribed degree and diameter, the Moore bound is the upper bound of this order forany pair of fixed values (diameter and degree). If there exists a graph whose order coincideswith this bound we call it a Moore graph.A bipartite graph G = (V, E) with V = V1 ∪ V2 is biregular if all the vertices of a stable setVi have the same degree ri for i = 1, 2. In this work, we study the diameter/degree problemin this context, introduced in 1983 by Yebra, Fiol, and F`abrega.The authors of that paper give a Moore bound for bipartite biregular graphs, called theMoore-like bound. In this work, we proved that for some cases of odd diameter it is impossibleto attain this bound and we give a new bound for these specific cases, we said that weimprove the Moore-like bound. We also propose some constructions of large bipartitebiregular graphs, some of them attaining our new Moore-like bound.