Neighbor Connectivity of the Alternating Group Graph - Abdullah, Mohammad (2021)
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.