Assessing the Super\(P_k\)-Connectedness of Crossed Cubes

Abstract

互连网络是可编程系统，用于在网络组件和/或终端之间传输数据或消息。网络的拓扑通常由图表建模。秩序路径K.in a graphG是一系列K.distinct vertices, denoted by\（p_k = \ langle v_1，v_2，\ cdots，v_k \ rangle \）, in which any two consecutive vertices are adjacent. The connectivity is a classic index to assess the level of network reliability and fault tolerance. For\（k \ ge 2 \）， 一套F顶点子集G是A.\(P_k\)- 否则if.\(G-F\)is disconnected, and each element ofFhappens to induce a\(P_k\)-subgraph inG。A connected graphG是超级的\(P_k\)- 如果最小的组件\(G-F\)是A.singleton for every minimum\(P_k\)-切FofG。A network with smaller diameter can reduce its communication delay in a worst-case perspective. The crossed cube\（cq_n \）是A.hypercube variant whose diameter is about one half of that of the hypercube. This paper is inspired to discover whether\（cq_n \）是超级的\(P_k\)-connected for\(k=2,3,4\)。