The r -Restricted Connectivity of Hyper Petersen Graphs

The connectivity of a multiprocessor system or an interconnection network plays an important role in measuring the fault tolerance of the network. As a famous topology structure of interconnection networks, the hyper petersen graph HP_{n} has many good properties. In this paper, we show that the r -restricted connectivity of HP_{n} is -\frac {1}{2}r^{2}+\left({n -\frac {3}{2}}\right)r+n and HP_{n} is two super r -restricted connected for n\geq 4 and 0\leq r\leq n-3 .