Regular Connected Bipancyclic Spanning Subgraphs of Torus Networks.

It is well known that an n-dimensional torus T = T(k(1), k(2), ..., k(n)) is Hamiltonian. Then the torus T contains a spanning subgraph which is 2-regular and 2-connected. In this paper, we explore a strong property of torus networks. We prove that for any even integer k with 3 <= k <= 2n, the torus T (n >= 3) contains a spanning subgraph which is k-regular, k-connected and bipancyclic; and if k is odd, the result holds when some k(i) is even.