Classifying Seven-Valent Symmetric Graphs of Order 8pq

A graph is symmetric if its automorphism group is transitive on the arcs of the graph. Guo et al. determined all of the connected seven-valent symmetric graphs of order 8p for each prime p. We shall generalize this result by determining all of the connected seven-valent symmetric graphs of order 8pq with p and q to be distinct primes. As a result, we show that for each such graph of Γ, it is isomorphic to one of seven graphs.