Fault-tolerant vertex-pancyclicity of locally twisted cubes LTQnLTQn

• The structure of LTQnLTQn and some definitions and notations.
• We introduce some properties of LTQnLTQn.
• Investigates the fault-tolerant vertex-pancyclicity of LTQnLTQn.
• Prove that LTQnLTQn is nn-3 fault-tolerant 4-vertex-pancyclicity.

The nn-dimensional locally twisted cube LTQnLTQn is a variant of the hypercube, which possesses some properties superior to the hypercube. This paper investigates the fault-tolerant vertex-pancyclicity of LTQnLTQn, and shows that if LTQnLTQn (n⩾3n⩾3) contains at most n−3n−3 faulty vertices and/or edges then, for any fault-free vertex uu and any integer ℓℓ with 4⩽ℓ⩽2n−fv4⩽ℓ⩽2n−fv except for 5, there is a fault-free cycle of length ℓℓ containing the vertex uu, where fvfv is the number of faulty vertices. The result is optimal in some senses.