The Restricted Connectivity of Locally Twisted Cubes

In this paper, we study the restricted connectivity and restricted fault-diameters of locally twisted cubes under the condition that each node has at least one fault-free neighbor. First, we prove that under the condition that if each node of an n-dimensional locally twisted cube LTQ_n has at least one fault-free neighbor its restricted connectivity is 2n-2, the same as that of the n-dimensional hypercube. Then, we give an upper bound on the restricted fault-diameter of LTQ_n, that is, the restricted fault-diameter of LTQ_n is no more than the fault-diameter of LTQ_n plus 6.