Bounds for neighbor connectivity of Cayley graphs generated by trees and unicyclic graphs

The neighbor connectivity refers to the minimum number of vertices whose removal, along with their neighbors, causes a previously connected graph to become disconnected. In this paper we focus on Cayley graphs constructed from the symmetric group S n . We investigate the bounds of the neighbor connectivity for two cases: when the generating graph is a tree, and when it is a unicyclic graph with a unique cycle of length m , specifically considering cases where m = 3 , m = n - 1 , or m = n .