Fault-tolerant vertex-pancyclicity of locally twisted cubes [formula omitted

Abstract

The n-dimensional locally twisted cube LTQn is a variant of the hypercube, which possesses some properties superior to the hypercube. This paper investigates the fault-tolerant vertex-pancyclicity of LTQn, and shows that if LTQn (n⩾3) contains at most n−3 faulty vertices and/or edges then, for any fault-free vertex u and any integer ℓ with 4⩽ℓ⩽2n−fv except for 5, there is a fault-free cycle of length ℓ containing the vertex u, where fv is the number of faulty vertices. The result is optimal in some senses.