Some Properties of Proper Power Graphs in Finite Abelian Groups

Autor:	G, Dhawlath., V, Raja.
Rok vydání:	2024
Předmět:	Mathematics - Group Theory Mathematics - Combinatorics 05 G.2
Druh dokumentu:	Working Paper
Popis:	The power graph of a group $G$, denoted as $P(G)$, constitutes a simple undirected graph characterized by its vertex set $G$. Specifically, vertices $a,b$ exhibit adjacency exclusively if $a$ belongs to the cyclic subgroup generated by $b$ or vice versa. The corresponding proper power graph of $G$ is obtained by taking $P(G)$ and removing a vertex corresponding to the identity element, which is denoted as $P^*(G)$. In the context of finite abelian groups, this article establishes the sufficient and necessary conditions for the proper power graph's connectedness. Moreover, a precise upper bound for the diameter of $P^*(G)$ in finite abelian groups is provided with sharpness. This article also explores the study of vertex connectivity, center, and planarity. Comment: 12 pages and 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2401.11873 Zobrazit plný text záznamu View this record from Arxiv