Let Γ be a finite connected G-vertex-transitive graph and let v be a vertex of Γ. If the permutation group induced by the action of the vertex-stabiliser G v on the neighbourhood Γ(v) is permutation isomorphic to L, then (Γ,G) is said to be locally L. A permutation group L is graph-restrictive if there exists a constant c(L) such that, for every locally L pair (Γ,G) and a vertex v of Γ, the inequality |G v |≤c(L) holds. We show that an intransitive group is graph-restrictive if and only if it is semiregular. © 2013 Springer Science+Business Media New York.

Spiga, P., Verret, G. (2014). On intransitive graph-restrictive permutation groups. JOURNAL OF ALGEBRAIC COMBINATORICS, 40(1), 179-185 [10.1007/s10801-013-0482-5].

### On intransitive graph-restrictive permutation groups

#### Abstract

Let Γ be a finite connected G-vertex-transitive graph and let v be a vertex of Γ. If the permutation group induced by the action of the vertex-stabiliser G v on the neighbourhood Γ(v) is permutation isomorphic to L, then (Γ,G) is said to be locally L. A permutation group L is graph-restrictive if there exists a constant c(L) such that, for every locally L pair (Γ,G) and a vertex v of Γ, the inequality |G v |≤c(L) holds. We show that an intransitive group is graph-restrictive if and only if it is semiregular. © 2013 Springer Science+Business Media New York.
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Graph-restrictive; Semiregular; Vertex-transitive; Discrete Mathematics and Combinatorics; Algebra and Number Theory
English
2014
40
1
179
185
reserved
Spiga, P., Verret, G. (2014). On intransitive graph-restrictive permutation groups. JOURNAL OF ALGEBRAIC COMBINATORICS, 40(1), 179-185 [10.1007/s10801-013-0482-5].
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/10281/133215`
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