| Abstract: | A Hamiltonian graph G is panpositionably Hamiltonian if for any two distinct vertices x and y of G, it contains a Hamiltonian cycle C such that d(C)(x,y) = l for any integer l satisfying d(G)(x,y) <= l <= inverted right perpendicular vertical bar V(G)vertical bar/2inverted left perpendicular, where d(G)(x,y) (respectively, d(C)(x,y)) denotes the distance between vertices x and y in G (respectively, on C), and vertical bar V(G)vertical bar is the total number of vertices in G. As the importance of Hamiltonian properties for data communication between units in parallel and distributed systems, the panpositionable Hamiltonicity involves more flexible cycle embedding for message transmission. This paper shows that for two arbitrary nodes x and y of the n-dimensional locally twisted cube LTQ(n), n >= 4, and for any integer l is an element of {d} boolean OR {d + 2, d + 3, d + 4, ..., 2(n-1)}, where d = d(LTQn)(x,y), there exists a Hamiltonian cycle C of LTQ(n) such that d(C)(x,y) = l. (C) 2013 Elsevier Inc. All rights reserved. |
