2020/06/03 by C. Dalfó, Dalfó, C., M.A. Fiol +5
Computer Science · Mathematics · #05C12 #05C25 #05C35 #90B10 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Interconnection Networks and Systems
paper · pdf · doi:10.48550/arxiv.2006.02897
openalex publication_date 2020/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the case in which mixed graphs (with both directed and undirected edges) are Cayley graphs of Abelian groups. In this case, some Moore bounds were derived for the maximum number of vertices that such graphs can attain. We first show these bounds can be improved if we know more details about the order of some elements of the generating set. Based on these improvements, we present some new families of mixed graphs. For every fixed value of the degree, these families have an asymptotically large number of vertices as the diameter increases. In some cases, the results obtained are shown to be optimal.