One-to-one disjoint path covers on alternating group graphs

The alternating group graph, denoted by AGn, is one of the popular interconnection networks, which has many attractive properties. In this paper, we prove that for any two distinct nodes μ and ν, there exist m node-disjoint paths for any integer n≥3 with 1≤m≤2n−4 whose union covers all the nodes of AGn. For any node of AGn has exactly 2n−4 neighbors, 2n−4 is the maximum number of node-disjoint paths can be constructed in AGn.