On bipartite biregular Moore graphs

• Gabriela Araujo-Pardo ^[1] ; Cristina Dalfó ^[2] ; Miguel Angel Fiol ^[3] ; Nacho López ^[2]
  1. [1] Universidad Nacional Autónoma de México

     Universidad Nacional Autónoma de México

     México

     
  2. [2] Universitat de Lleida

     Universitat de Lleida

     Lérida, España

     
  3. [3] Universitat Politècnica de Catalunya

     Universitat Politècnica de Catalunya

     Barcelona, España

     

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• Localización: Discrete Mathematics Days 2022 / Luis Felipe Tabera Alonso (ed. lit.), 2022, ISBN 978-84-19024-02-2, págs. 274-279
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.