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

Abdallah, Mohamad (American University of Kuwait)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 12, No 2 (2024): Electronic Journal of Graph Theory and Applications

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 Sn. 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.