Asymptotic enumeration of vertex-transitive graphs of fixed valency

Primož Potočnik, Pablo Spiga, Gabriel Verret

    Research output: Contribution to journalArticle

    4 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 languageEnglish
    Pages (from-to)221-240
    Number of pages20
    JournalJournal of Combinatorial Theory. Series B
    Volume122
    DOIs
    Publication statusPublished - 1 Jan 2017

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