Fault-tolerant edge-pancyclicity of locally twisted cubes

Abstract

The n-dimensional locally twisted cube LTQ n is a new 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 ⩾ 3) contains at most n − 3 faulty vertices and/or edges then, for any fault-free edge e and any integer ℓ with 6 ⩽ ℓ ⩽ 2 n − 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. The proof is based on the recursive structure of LTQ n .