## Pentavalent arc-transitive graphs of order $$2p^{2}q$$.(English)Zbl 1401.05138

Summary: In this paper, we complete a classification of pentavalent arc-transitive graphs of order $$2p^{2}q$$, where $$p$$ and $$q$$ are distinct odd primes. This result involves a subclass of pentavalent arc-transitive graphs of cube-free order.

### MSC:

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

### Keywords:

arc-transitive graph; Cayley graph; cube-free order

Magma
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### References:

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