Neighbor Connectivity of the Alternating Group Graph

Given a graph G = (V,E), its neighbor connectivity is the least number of vertices whose deletion along with their neighbors results in a disconnected, complete, or empty graph. The edge neighbor connectivity is the least number of edges whose deletion along with their endpoints results in a disconnected, complete, or empty graph. In this paper, we determine the neighbor connectivity κNB and the edge neighbor connectivity λNB of the alternating group graph. We show that κNB(AGn) = λNB(AGn) = n - 2, where AGn is the n-dimensional alternating group graph.