On finite edge-primitive and edge-quasiprimitive graphs

Details On finite edge-primitive and edge-quasiprimitive graphs On finite edge-primitive and edge-quasiprimitive graphs

2009-09-14

arxiv.org/abs/0909.2473v1

Mathematics

Combinatorics

30 pages To appear in Journal of Combinatorial Theory Series B

Scientific paper

Many famous graphs are edge-primitive, for example, the Heawood graph, the Tutte--Coxeter graph and the Higman--Sims graph. In this paper we systematically analyse edge-primitive and edge-quasiprimitive graphs via the O'Nan--Scott Theorem to determine the possible edge and vertex actions of such graphs. Many interesting examples are given and we also determine all $G$-edge-primitive graphs for $G$ an almost simple group with socle $PSL(2,q)$.

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