Strongly Menger Connectedness of a Class of Recursive Networks.

This article focuses on the strongly Menger (edge) connectedness of a class of \(r\)-dimensional recursive networks called RNCG \(G_r\), which include triangles and encompass well-known networks such as data center networks DCell, generalized DCell, and dragonfly interconnection networks. Strongly Menger-node-connectedness and strongly Menger-edge-connectedness are defined based on the existence of internally node-disjoint and edge-disjoint paths between nodes after the removal of faulty nodes or edges, respectively. The authors prove that \(G_r\) is \((rl - l - 1)\)-strongly Menger-node-connected, \([k + (r-1)l - 2]\)-strongly Menger-edge-connected of order 1, and \([2k + 2(r-1)l - 6]\)-strongly Menger-edge-connected of order 2, with these bounds shown to be sharp. These results extend previous studies that primarily addressed triangle-free networks, providing reliability measures applicable to a broader class of recursive networks with triangles.