2025/04/01 by Ramesh Prasad Panda, Panda, Ramesh Prasad
Mathematics · Computer Science · #Finite Group Theory Research #Interconnection Networks and Systems #Advanced Graph Theory Research
paper · pdf · doi:10.48550/arxiv.2504.00571
Consider a graph Γ. A set S of vertices in Γ is called a cyclic vertex cutset of Γ if Γ- S is disconnected and has at least two components containing cycles. If Γ has a cyclic vertex cutset, then it is said to be cyclically separable. The cyclic vertex connectivity is the minimum cardinality of a cyclic vertex cutset of Γ. The power graph P(G) of a group G is the undirected simple graph with vertex set G and two distinct vertices are adjacent if one of them is a positive power of the other. If G is a cyclic, dihedral, or dicyclic group, we determine the order of G such that P(G) is cyclically separable. Then we characterize the equality of vertex connectivity and cyclic vertex connectivity of P(G) in terms of the order of G.