Reliability Analysis Based On The Dual-Cist In Shuffle-Cubes

Let T-1, T-2, ..., T-k be k spanning trees of the graph G. They are called completely independent spanning trees (CISTs for short) if the paths joining every pair of vertices x and y in any two trees have neither vertex nor edge in common, except for x and y. In particular, two CISTs are called a dual CIST. The construction of a dual-CIST in a network has applications in the fault-tolerance of data transmission and the establishment of a protection routing. It has been proved that determining if a graph G admits a dual-CIST is NP-complete. In this paper, we show the existence of a dual-CIST in the n-dimensional shuffle-cube SQ(n) with n = 4k + 2 and k >= 1. Furthermore, recursive construction algorithms for the dual-CIST in SQ(n) are given. (C) 2021 Elsevier Inc. All rights reserved.