On 7-valent symmetric graphs of order 2pq and 11-valent symmetric graphs of order 4pq

A graph is said to be symmetric if its automorphism group is transitive on its arcs. This article is one of a series of articles devoted to characterizing prime-valent arc-transitive graphs of square-free order or twice square-free order. In this article, we determine all 7-valent symmetric graphs of order 2pq and 11-valent symmetric graphs of order 4pq.