The g-extra edge connectivity is a novel measure of the reliability of an interconnection network. In this paper, we study the {2, 3}-extra edge connectivity of the star graph Sn. We show that λg(Sn) = (g+1)n-3g-1 for g = 2, 3 and n ≥ 4. This means that, to become a disconnected graph with every component having more than g vertices, we need to delete at least (g+1)n-3g-1 edges from Sn for g = 2, 3 and n ≥ 4. We also remark that the equation λg(Sn) = (g+1)n-3g-1 does not hold for g = 4.

Because the Internet has been widely applied in various fields, more and more network security issues emerge and catch people's attention. However, adversaries often hide themselves by spoofing their own IP addresses and then launch attacks. For this reason, researchers have proposed a lot of traceback schemes to trace the source of these attacks. Some use only one packet in their packet logging schemes to achieve IP tracking. Others combine packet marking with packet logging and therefore create hybrid IP traceback schemes demanding less storage but requiring a longer search. In this paper, we propose a new hybrid IP traceback scheme with efficient packet logging aiming to have a fixed storage requirement for each router (under 320 KB, according to CAIDA's skitter data set) in packet logging without the need to refresh the logged tracking information and to achieve zero false positive and false negative rates in attack-path reconstruction. In addition, we use a packet's marking field to censor attack traffic on its upstream routers. Lastly, we simulate and analyze our scheme, in comparison with other related research, in the following aspects: storage requirement, computation, and accuracy.

A graph G is pancyclic if, for every 4 ¿ l ¿ |V (G)|, G has a cycle of length l. A graph G is edge-pancyclic if, for an arbitrary edge e of G and every 4 ¿ l ¿ |V(G)|, G has a cycle of length l containing e. A graph G is node-pancyclic if, for an arbitrary node u of G and every 4 ¿ l ¿ |V (G)|, G has a cycle of length l containing u. The twisted cube is an important variant of the hypercube. Recently, Fan et al. proved that the n-dimensional twisted cube TQnis edge-pancyclic for every n ¿ 3. They also asked if TQnis edge-pancyclic with (n-3) faults for n ¿ 3. We find that TQnis not edge-pancyclic with only one faulty edge for any n ¿ 3. Then we prove that TQnis node-pancyclic with (\langle n/2\rangle - 1) faulty edges for every n ¿ 3. The result is optimal in the sense that with \langle n/2\rangle faulty edges, the faulty TQnis not node-pancyclic for any n ¿ 3.

The star graph has been an attractive interconnection network, and possesses many nice properties. In this paper, we consider the cycle embedding problem in star graphs with conditional edge faults. We show that there exist cycles of all even lengths from 6 to n! in an n-dimensional star graph with ¿ 2n - 7 edge faults in which each vertex is incident with at least two healthy edges for n ¿ 4.