THE FINITE VERTEX-PRIMITIVE AND VERTEX-BIPRIMITIVE s-TRANSITIVE GRAPHS FOR s ≥ 4
نویسنده
چکیده
A complete classification is given for finite vertex-primitive and vertex-biprimitive s-transitive graphs for s ≥ 4. The classification involves the construction of new 4-transitive graphs, namely a graph of valency 14 admitting the Monster simple group M, and an infinite family of graphs of valency 5 admitting projective symplectic groups PSp(4, p) with p prime and p ≡ ±1 (mod 8). As a corollary of this classification, a conjecture of Biggs and Hoare (1983) is proved.
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