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arXiv · 2001.03916

On the existence and the enumeration of bipartite regular representations of Cayley graphs over abelian groups

Jia-Li Du·Yan-Quan Feng·Pablo Spiga
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Abstract

In this paper we are interested in the asymptotic enumeration of bipartite Cayley digraphs and Cayley graphs over abelian groups. Let $A$ be an abelian group and let $\iota$ be the automorphism of $A$ defined by $a^\iota=a^{-1}$, for every $a\in A$. A Cayley graph $\Cay(A, S)$ is said to have an automorphism group as small as possible if $\Aut(\Cay(A,S)) = \langle A,\iota\rangle$. In this paper, we show that, except for two infinite families, almost all bipartite Cayley graphs on abelian groups have automorphism group as small as possible. We also investigate the analogous question for bipartite Cayley digraphs.

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Jia-Li Du, Yan-Quan Feng, Pablo Spiga. 2020-01-12. On the existence and the enumeration of bipartite regular representations of Cayley graphs over abelian groups. https://arxiv.org/abs/2001.03916

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