An interconnection network is usually modeled as a graph, in which vertices and edges correspond to processors and communication links, respectively. Connectivity is an important metric for fault tolerance of interconnection networks. A graph [Formula: see text] is said to be maximally local-connected if each pair of vertices [Formula: see text] and [Formula: see text] are connected by [Formula: see text] vertex-disjoint paths. In this paper, we show that Cayley graphs generated by [Formula: see text]([Formula: see text]) transpositions are [Formula: see text]-fault-tolerant maximally local-connected and are also [Formula: see text]-fault-tolerant one-to-many maximally local-connected if their corresponding transposition generating graphs have a triangle, [Formula: see text]-fault-tolerant one-to-many maximally local-connected if their corresponding transposition generating graphs have no triangles. Furthermore, under the restricted condition that each vertex has at least two fault-free adjacent vertices, Cayley graphs generated by [Formula: see text]([Formula: see text]) transpositions are [Formula: see text]-fault-tolerant maximally local-connected if their corresponding transposition generating graphs have no triangles.

中文翻译：

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由转置生成的凯莱图上的容错最大局部连通性

互连网络通常被建模为图，其中顶点和边分别对应于处理器和通信链路。连通性是互连网络容错的重要指标。如果每对顶点 [Formula: see text] 和 [Formula: see text] 由 [Formula: see text] 顶点不相交的路径连接，则图 [Formula: see text] 被认为是最大局部连接的。在本文中，我们证明了由[公式：见文本]（[公式：见文本]）转置生成的凯莱图是[公式：见文本]-容错最大局部连接的，也是[公式：见文本] -容错的一对多最大局部连接，如果它们对应的转置生成图有一个三角形，[公式：见文本]-容错的一对多最大局部连接，如果它们对应的转置生成图没有三角形。此外，在每个顶点至少有两个无故障相邻顶点的限制条件下，[公式：见文]（[公式：见文]）转置生成的凯莱图是[公式：见文]最大容错的如果它们对应的转置生成图没有三角形，则局部连接。