Abelian Cayley digraphs with asymptotically large order for any given degree

2015/02/10 by F. Aguiló-Gost, M.A. Fiol, Aguiló, F. +3
Mathematics · Computer Science · #Graph theory and applications #Cellular Automata and Applications #Advanced Graph Theory Research

paper · doi:10.48550/arxiv.1502.02744

Abstract

Abelian Cayley digraphs can be constructed by using a generalization to Zⁿ of the concept of congruence in Z. Here we use this approach to present a family of such digraphs, which, for every fixed value of the degree, have asymptotically large number of vertices as the diameter increases. Up to now, the best known asymptotically dense results were all non-constructive.

Related

• New results on the degree/diameter problem of mixed Abelian Cayley graphs
• Large Cayley graphs of small diameter
• Higher diameters of Cayley digraphs
• Asymptotic enumeration of Cayley digraphs
• The Dilating Method for Cayley digraphs on finite Abelian groups