Abstract
A graph is said to be symmetric if its automorphism group acts transitively on its arcs. In this paper, all connected pentavalent symmetric graphs of order 2pq are classified, where p,q are distinct primes. It follows from the classification that there are two connected pentavalent symmetric graphs of order 4p, and that for odd primes p and q, there is an infinite family of connected pentavalent symmetric graphs of order 2pq with solvable automorphism groups and there are seven sporadic ones with nonsolvable automorphism groups.
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