Pentavalent symmetric graphs of order \(2pq\)
In this paper, all connected pentavalent symmetric (1-arc-transitive) graphs of order \(2pq\) are classified, where \(p\) and \(q\) are distinct primes. It follows from the classification that there are two such graphs of order \(4p\) and, for odd primes \(p\) and \(q\), there is an infinite family of connected graphs of order \(2pq\) with solvable automorphism groups and there are seven sporadic ones with nonsolvable automorphism groups. The paper uses sophisticated group theoretic tools and the Sabidussi construction of 1-arc-transitive graphs as coset graphs Cos\((G,H,HaH)\) with \(H\leq G\), \(a^2\in H\) and \(\langle H, a \rangle = G\). The Magma computer algebra system is also used to determine when the coset graphs constructed are isomorphic.
scientific article; zbMATH DE number 5961737
scientific article