Symmetric graphs of order a product of two distinct primes
A simple undirected graph \(\Gamma\) is said to be symmetric if its automorphism group \(\Aut\Gamma\) is transitive on the set of ordered pairs of adjacent vertices of \(\Gamma\), and \(\Gamma\) is said to be imprimitive if \(\Aut\Gamma\) acts imprimitively on the vertices of \(\Gamma\). Let \(k\) and \(p\) be distinct primes with \(k< p\). This paper gives a classification of all imprimitive symmetric graphs on \(kp\) vertices for \(k\geq 5\). The cases \(k<5\) have been treated previously by Cheng and Oxley \((k=2)\) and the second and third authors \((k=3)\) (see item Zbl 0793.05074 below), and the classification of primitive symmetric graphs on \(kp\) vertices with \(k\geq 5\) was done by the first and third authors (see the following item Zbl 0793.05072).
scientific article; zbMATH DE number 572452