Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
436159 | Theoretical Computer Science | 2015 | 15 Pages |
In 1993, Fernandes and Kanevsky proposed an important structure for interconnection networks, WKR Pyramid Networks (WKP(d,t,L)WKP(d,t,L), for short). These are constructed by taking difference size WK-recursive network (WK(d,tn)WK(d,tn), for short) as difference layers. That study discussed the orders, sizes and connectivity of WKP(d,t,L)WKP(d,t,L) for any integers d≥1,t≥1d≥1,t≥1 and L≥1L≥1. The basic WK-recursive pyramid, denoted by WKP(d,L)WKP(d,L), is a basic version of WKP(d,t,L)WKP(d,t,L) such that t=1t=1. In WKP(d,L)WKP(d,L), each vertex has exactly d children and the n th layer is isomorphic to a WK(d,n)WK(d,n). In this paper, we show that WKP(d,L)WKP(d,L) is Hamiltonian-connected for any two integers, d≥3d≥3 and L≥1L≥1, and it is also (d−2)(d−2)-node Hamiltonian for any two integers, d≥2d≥2 and L≥1L≥1.