A List for Vertex-Primitive Symmetric Graphs of Order \(6p\)

Abstract

The aim of this paper is to classify the vertex-primitive symmetric graphs of order \(6p\). These works were essentially done in \([1]\). But in \([1]\) there is no such situation: \(G = \mathrm{PSL}(2, 13)\) acting on the set of cosets of subgroup \(H \cong D_{14}\). Then \(m = |\Omega| = 78 = 6p\), \(G\) has rank \(9\), and the sub-orbits of \(G\) have one of length \(1\), five of length \(7\), and three of length \(14\). In this paper, we give a complete list of symmetric graphs of order \(6p\).