Abelian Cayley Digraphs with Asymptotically Large Order for Any Given Degree

Francesc Aguiló, Miquel Àngel Fiol, Sonia Pérez

Abstract


Abelian Cayley digraphs can be constructed by using a generalization to $\mathbb{Z}^n$ of the concept of congruence in $\mathbb{Z}$. 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 large dense results were all non-constructive.

Keywords


Cayley digraph; Abelian group; Degree/diameter problem; Congruences in Z$^n$; Smith normal form

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