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ISSN 1088-6850(e) ISSN 0002-9947(p)

The finite vertex-primitive and vertex-biprimitive -transitive graphs for $s\ge4$

Author(s): Cai Heng Li
Journal: Trans. Amer. Math. Soc. 353 (2001), 3511-3529.
MSC (2000): Primary 05C25, 20B05
Posted: April 24, 2001
MathSciNet review: 1837245
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Abstract: A complete classification is given for finite vertex-primitive and vertex-biprimitive -transitive graphs for $s\ge4$ . The classification involves the construction of new 4-transitive graphs, namely a graph of valency 14 admitting the Monster simple group $\text{M}$ , and an infinite family of graphs of valency 5 admitting projective symplectic groups $\text{PSp}(4,p)$ with prime and $p\equiv\pm1$ (mod 8). As a corollary of this classification, a conjecture of Biggs and Hoare (1983) is proved.

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