Restricted Fault Diameter of Hypercube Networks

This paper studies restricted fault diameter of the n-dimensional hypercube networks Qn (n ≥ 2). It is shown that for arbitrary two vertices x and y with the distance d in Qn and any set F with at most 2n− 3 vertices in Qn −{x, y}, if F contains neither of neighbor-sets of x and y in Qn, then the distance between x and y in Qn − F is given by D(Qn − F ;x, y)   = 1, for d = 1; ≤ d + 4, for 2 ≤ d ≤ n − 2, n ≥ 4; ≤ n + 1, for d = n − 1, n ≥ 3;