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.

Potočnik, P., Spiga, P., Verret, G. (2015). Bounding the order of the vertex-stabiliser in 3-valent vertex-transitive and 4-valent arc-transitive graphs. JOURNAL OF COMBINATORIAL THEORY, 111, 148-180 [10.1016/j.jctb.2014.10.002].

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

SPIGA, PABLO
Secondo
;
2015

Abstract

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.
Articolo in rivista - Articolo scientifico
Arc-transitive; Locally-dihedral; Valency 3; Valency 4; Vertex-transitive; Discrete Mathematics and Combinatorics; Theoretical Computer Science; Computational Theory and Mathematics
English
2015
111
148
180
reserved
Potočnik, P., Spiga, P., Verret, G. (2015). Bounding the order of the vertex-stabiliser in 3-valent vertex-transitive and 4-valent arc-transitive graphs. JOURNAL OF COMBINATORIAL THEORY, 111, 148-180 [10.1016/j.jctb.2014.10.002].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/133239
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