Edge-bipancyclicity of star graphs under edge-fault tolerant

The star graph Sn is one of the most famous interconnection networks. It has been shown by Li [T.-K. Li, Cycle embedding in star graphs with edge faults, Appl. Math. Comput. 167 (2005) 891–900] that Sn contains a cycle of length from 6 to n! when the number of fault edges in the graph does not exceed n − 3. In this paper, we improve this result by showing that for any edge subset F of Sn with ∣F∣ ⩽ n − 3 every edge of Sn − F lies on a cycle of every even length from 6 to n! provided n ⩾ 3.