On finite edge-primitive and edge-quasiprimitive graphs

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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