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On weakly symmetric graphs of order twice a prime. (English) Zbl 0583.05032

A graph is weakly symmetric if its automorphism group is transitive on both its vertex-set and its edge-set. C.-Y. Chao [Trans. Am. Math. Soc. 158, 247-256 (1971; Zbl 0217.024)] characterized all weakly symmetric graphs of prime order and showed that such graphs are also transitive on directed edges. This paper determines all weakly symmetric graphs of order twice a prime and shows that these graphs too are directed-edge-transitive. The proof of this result relies on several important group-theoretic results including the recently-completed classification of finite simple groups.

MSC:

05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures
20D05 Finite simple groups and their classification

Citations:

Zbl 0217.024
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References:

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