This paper discusses a family of graphs, called Praeger-Xu graphs and denoted $\mathrm{PX}(n,k)$ here, introduced by C.E. Praeger and M.-Y. Xu in 1989. These tetravalent graphs are distinguished by having large symmetry groups; their vertex-stabilizers can be arbitrarily larger than the number of vertices in the graph. This paper does the following: (1) exhibits a connection between vertex-transitive groups of symmetries in a Praeger-Xu graph and certain linear codes, (2) characterizes those linear codes, (3) characterizes Praeger-Xu graphs $\mathrm{PX}(n,k)$ which are Cayley, (4) shows that every $\mathrm{PX}(n,k)$ is quasi-Cayley, and (5) constructs an infinite family of Praeger-Xu graphs in which a smallest vertex-transitive group of symmetries has arbitrarily large vertex-stabiliser.

本文讨论了一系列图，称为 Praeger-Xu 图，表示为 $\mathrm{PX}(n,克)$在这里，由 CE Praeger 和 M.-Y 介绍。Xu 在 1989 年。这些四价图的特点是具有大的对称群；它们的顶点稳定器可以任意大于图中的顶点数。本文做了以下工作：(1) 展示了 Praeger-Xu 图中的顶点传递对称群与某些线性代码之间的联系，(2) 表征这些线性代码，(3) 表征 Praeger-Xu 图$\mathrm{PX}(n,克)$ 是 Cayley，(4) 表明，每 $\mathrm{PX}(n,克)$ 是拟凯莱，并且 (5) 构造了一个无限的 Praeger-Xu 图族，其中最小的顶点传递对称群具有任意大的顶点稳定子。