Bounding the order of the vertex-stabiliser in 3-valent vertex-transitive and 4-valent arc-transitive graphs

P. Potočnik, P. Spiga, Gabriel Verret

    Research output: Contribution to journalArticle

    15 Citations (Scopus)

    Abstract

    © 2014 Elsevier Inc. The main result of this paper is that, if Γ is a connected 4-valent G-arc-transitive graph and v is a vertex of Γ, then either Γ is part of a well-understood infinite family of graphs, or |Gv|≤2436 or 2|Gv|log2(|Gv|/2)≤|VΓ| and that this last bound is tight. As a corollary, we get a similar result for 3-valent vertex-transitive graphs.
    Original languageEnglish
    Pages (from-to)148-180
    Number of pages33
    JournalJournal of Combinatorial Theory. Series B
    Volume111
    DOIs
    Publication statusPublished - Mar 2015

    Fingerprint

    Arc-transitive Graph
    Vertex-transitive
    Vertex-transitive Graph
    Vertex of a graph
    Corollary
    Graph in graph theory
    Family

    Cite this

    @article{ca452c38cb964aac9bc1f1111761b1d1,
    title = "Bounding the order of the vertex-stabiliser in 3-valent vertex-transitive and 4-valent arc-transitive graphs",
    abstract = "{\circledC} 2014 Elsevier Inc. The main result of this paper is that, if Γ is a connected 4-valent G-arc-transitive graph and v is a vertex of Γ, then either Γ is part of a well-understood infinite family of graphs, or |Gv|≤2436 or 2|Gv|log2(|Gv|/2)≤|VΓ| and that this last bound is tight. As a corollary, we get a similar result for 3-valent vertex-transitive graphs.",
    author = "P. Potočnik and P. Spiga and Gabriel Verret",
    year = "2015",
    month = "3",
    doi = "10.1016/j.jctb.2014.10.002",
    language = "English",
    volume = "111",
    pages = "148--180",
    journal = "Journal of combinatorial Theory Series B",
    issn = "0095-8956",
    publisher = "Academic Press",

    }

    Bounding the order of the vertex-stabiliser in 3-valent vertex-transitive and 4-valent arc-transitive graphs. / Potočnik, P.; Spiga, P.; Verret, Gabriel.

    In: Journal of Combinatorial Theory. Series B, Vol. 111, 03.2015, p. 148-180.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - Bounding the order of the vertex-stabiliser in 3-valent vertex-transitive and 4-valent arc-transitive graphs

    AU - Potočnik, P.

    AU - Spiga, P.

    AU - Verret, Gabriel

    PY - 2015/3

    Y1 - 2015/3

    N2 - © 2014 Elsevier Inc. The main result of this paper is that, if Γ is a connected 4-valent G-arc-transitive graph and v is a vertex of Γ, then either Γ is part of a well-understood infinite family of graphs, or |Gv|≤2436 or 2|Gv|log2(|Gv|/2)≤|VΓ| and that this last bound is tight. As a corollary, we get a similar result for 3-valent vertex-transitive graphs.

    AB - © 2014 Elsevier Inc. The main result of this paper is that, if Γ is a connected 4-valent G-arc-transitive graph and v is a vertex of Γ, then either Γ is part of a well-understood infinite family of graphs, or |Gv|≤2436 or 2|Gv|log2(|Gv|/2)≤|VΓ| and that this last bound is tight. As a corollary, we get a similar result for 3-valent vertex-transitive graphs.

    U2 - 10.1016/j.jctb.2014.10.002

    DO - 10.1016/j.jctb.2014.10.002

    M3 - Article

    VL - 111

    SP - 148

    EP - 180

    JO - Journal of combinatorial Theory Series B

    JF - Journal of combinatorial Theory Series B

    SN - 0095-8956

    ER -