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 kappa NB and the edge neighbor connectivity kappa NB of the alternating group graph. We show that lambda NB(AGn) = lambda(NB)(AG(n)) = n - 2, where AG(n) is the n-dimensional alternating group graph.