Cycle embedding in star graphs with more conditional faulty edges

Abstract

The star graph is one of the most attractive interconnection networks. The cycle embedding problem is widely discussed in many networks, and edge fault tolerance is an important issue for networks since edge failures may occur when a network is put into use. In this paper, we investigate the cycle embedding problem in star graphs with conditional faulty edges. We show that there exist fault-free cycles of all even lengths from 6 to n! in any n-dimensional star graph S n ( n ⩾ 4) with ⩽3 n − 10 faulty edges in which each node is incident with at least two fault-free edges. Our result not only improves the previously best known result where the number of tolerable faulty edges is up to 2 n − 7, but also extends the result that there exists a fault-free Hamiltonian cycle under the same condition.