The $r$ -Restricted Connectivity of Hyper Petersen Graphs

Abstract

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 − 1 2 r 2 + (n − 3 2)r + n and HP n is two super r-restricted connected for n ≥ 4 and 0 ≤ r ≤ n − 3. INDEX TERMS Interconnection network, connectivity, hyper petersen graph.