On The Reliability Of Double Generalized Petersen Graph

Let G be a graph with vertex set V(G)and edge set E(G).The super-connectivity(super-edge-connectivity)of a connected graph G is the minimum num-ber of vertices(edges)that need to be deleted from G in order to disconnect G with-out creating isolated vertices.The concept of double generalized Petersen graphs was introduced by Zhou and Feng(2012).In this paper,we determine when a double generalized Petersen graph is super-connected or super-edge-connected,and show that their super-connectivity and their super-edge-connectivity are both equal to four if n(?){2/k,3}.