Name
Abstract | ||
|---|---|---|
The locally twisted cube LTQ(n) is a variant of the hypercube Q(n), which was introduced by Yang et al. (2005) as an interconnection network for parallel computing. The symmetry of Q(n) is well-known, for example, it is an edge-transitive Cayley graph. However, the symmetry of LTQ(n) remains unclear. In this paper, we first prove that LTQ(n) with n >= 4 is isomorphic to a bi-Cayley graph of an elementary abelian 2-group Z(2)(n)(-1) of order 2(n-1), and then prove that the full automorphism group of LTQ(n) with n >= 4 is isomorphic to Z(2)(n-1). These show that LTQ(n) with n >= 4 is not edge-transitive, and its full automorphism group has exactly two orbits on the vertex set of LTQ(n) (and consequently it is not vertex-transitive and not a Cayley graph). What is more, the symmetry of LTQ(n) with n >= 4 also implies that it can be decomposed to two vertex-disjoint (n- 1)-dimensional hypercubes and a perfect matching. As an application, we obtain the k-extra connectivity and (k 1)-component connectivity with k <= n - 1 of LTQ(n), which generalize some previous works. (C) 2020 Elsevier B.V. All rights reserved. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.1016/j.dam.2020.09.009 | DISCRETE APPLIED MATHEMATICS |
Keywords | DocType | Volume |
Interconnection network, Locally twisted cubes, Bi-Cayley graphs, Extra connectivity, Component connectivity | Journal | 288 |
ISSN | Citations | PageRank |
0166-218X | 0 | 0.34 |
References | Authors | |
0 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Xuenan Chang | 1 | 0 | 0.34 |
| Jicheng Ma | 2 | 0 | 2.70 |
| Da-Wei Yang | 3 | 0 | 1.35 |