Pentavalent symmetric graphs of order

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 2 p q are classified, where p , q are distinct primes. It follows from the classification that there are two connected pentavalent symmetric graphs of order 4 p , and that for odd primes p and q , there is an infinite family of connected pentavalent symmetric graphs of order 2 p q with solvable automorphism groups and there are seven sporadic ones with nonsolvable automorphism groups.