Extreme Vertices of the Psi-Divisible Graph of the Group Z_{p^n}

Kumar, Amit
Kumar, Vinod
Sehgal, Amit

Journal of the Indonesian Mathematical Society
Vol. 32 No. 2 (2026): JUNE

The $\Psi$-divisible graph of a finite group $G$, denoted by $\Psi_G$ is a special type of simple undirected graph, in which the set of vertices contains non-trivial subgroups of $G$ and two distinct vertices $u$ and $v$ are adjacent if and only if $u$ is a proper subgroup of $v$ such that $\Psi(u)|\Psi(v)$ or $v$ is a proper subgroup of $u$ such that $\Psi(v)|\Psi(u)$. The existence of extreme vertices in the $\Psi$-divisible graph of the finite cyclic group $\mathbb{Z}_{p^n}$ is described in this article.