Imprimitive symmetric graphs, 3-arc graphs and 1-designs (Q1349118)

The author investigated symmetric graphs admitting an imprimitive automorphism group, under the framework of \textit{A. Gardiner} and \textit{C. E. Praeger} for imprimitive symmetric graphs established in [Proc. Lond. Math. Soc., III. Ser. 71, 524-546 (1995; Zbl 0837.05068)]. The main result of this paper is a proof that one class of symmetric graphs obtained by \textit{C. H. Li}, \textit{C. E. Praeger} and \textit{S. Zhou} [Math. Proc. Camb. Philos. Soc. 129, 19-34 (2000; Zbl 0958.05064)] may be described as a class of certain arc-graphs of their quotient graphs.