The super-connectivity of double generalized Petersen graphs

Abstract

The super--connectivity of a graph $ G $ is the minimum number of vertices whose removal disconnects the graph without isolating a vertex. In this paper, we prove that the super--connectivity of double generalized Petersen graph $ DP(n,k) $ is equal to four when $ n\geq 4 $, $ k\geq 1 $ and $ n\neq2k $.