2020/05/05 by Gabriela Araujo‐Pardo, Gabriela Araujo-Pardo, Araujo-Pardo, Gabriela +2
Computer Science · Engineering · Mathematics · #05C35 #51E15 #Advancements in Battery Materials #Combinatorics (math.CO) #FOS: Mathematics #Fiber-reinforced polymer composites #Interconnection Networks and Systems #math.CO #msc:05C35 #msc:51E15
paper · pdf · doi:10.48550/arxiv.2005.02427
arxiv created 2020/05/05 · openalex publication_date 2020/05/05 · arxiv updated 2020/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The modelling of interconnection networks by graphs motivated the study of several extremal problems that involve well known parameters of a graph (degree, diameter, girth and order) and ask for the optimal value of one of them while holding the other two fixed. Here we focus in \em bipartite Moore graphs\/, that is, bipartite graphs attaining the optimum order, fixed either the degree/diameter or degree/girth. The fact that there are very few bipartite Moore graphs suggests the relaxation of some of the constraints implied by the bipartite Moore bound. First we deal with \em local bipartite Moore graphs. We find in some cases those local bipartite Moore graphs with local girths as close as possible to the local girths given by a bipartite Moore graph. Second, we construct a family of (q+2)-bipartite graphs of order 2(q2+q+5) and diameter 3, for q a power of prime. These graphs attain the record value for q=9 and improve the values for q=11 and q=13.