# Asymptotic enumeration of vertex-transitive graphs of fixed valency

Primož Potočnik, Pablo Spiga, Gabriel Verret

Research output: Contribution to journalArticle

2 Citations (Scopus)

### Abstract

Let G be a group and let S be an inverse-closed and identity-free generating set of G. The Cayley graph Cay(G,S) has vertex-set G and two vertices u and v are adjacent if and only if uv−1∈S. Let CAYd(n) be the number of isomorphism classes of d-valent Cayley graphs of order at most n. We show that log⁡(CAYd(n))∈Θ(d(log⁡n)2), as n→∞. We also obtain some stronger results in the case d=3.

Original language English 221-240 20 Journal of Combinatorial Theory. Series B 122 https://doi.org/10.1016/j.jctb.2016.06.002 Published - 1 Jan 2017

### Fingerprint

Asymptotic Enumeration
Vertex-transitive Graph
Cayley Graph
Generating Set
Isomorphism Classes
If and only if
Closed
Vertex of a graph

### Cite this

Potočnik, Primož ; Spiga, Pablo ; Verret, Gabriel. / Asymptotic enumeration of vertex-transitive graphs of fixed valency. In: Journal of Combinatorial Theory. Series B. 2017 ; Vol. 122. pp. 221-240.
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Asymptotic enumeration of vertex-transitive graphs of fixed valency. / Potočnik, Primož; Spiga, Pablo; Verret, Gabriel.

In: Journal of Combinatorial Theory. Series B, Vol. 122, 01.01.2017, p. 221-240.

Research output: Contribution to journalArticle

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