Fault-tolerant edge-pancyclicity of locally twisted cubes LTQn

Abstract

The n-dimensional locally twisted cube LTQ_n is a variant of the hypercube, which possesses some properties superior to the hypercube. This paper investigates the fault-tolerant edge-pancyclicity of LTQ_n, and shows that if LTQ_n (n ≽ 5) contains at most n - 2 faulty vertices and/or edges then, for any fault-free edge e and any integer ℓ with 7 ≼ ℓ ≼ 2ⁿ — f_v there is a fault-free cycle of length ℓ containing the edge e, where f_v is the number of faulty vertices. The result is optimal in some senses. © 2020 Utilitas Mathematica Publishing Inc.. All rights reserved.