2025/01/21 by Panda, Ramesh Prasad, Ray, Papi
#05C25 #05C40 #20D15 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2501.12307
Let Γ be an undirected and simple graph. 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 each containing a cycle. If Γ has a cyclic vertex cutset, then it is said to be cyclically separable. For any finite group G, the order supergraph S(G) is the simple and undirected graph whose vertices are elements of G, and two vertices are adjacent if as elements of G the order of one divides the order of the other. In this paper, we characterize the finite nilpotent groups and various non-nilpotent groups, such as the dihedral groups, the dicyclic groups, the EPPO groups, the symmetric groups, and the alternating groups, whose order supergraphs are cyclically separable.