Characterizations of algebraic and vertex connectivity of power graph of finite cyclic groups

	Characterizations of algebraic and vertex connectivity of power graph of finite cyclic groups
Journal of Algebra and Related Topics
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 04 تیر 1404
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22124/jart.2025.28572.1719
نویسندگان
Ch. V. Visave^* ؛ R. P. Deore
, Department of Mathematics, University of Mumbai, Mumbai, India
چکیده
The Power graph of a group $G$ is a graph $\mathcal{P}(G)$ with vertex set $G$ and two vertices $x$ and $y$, $x \neq y$ are adjacent if there exists some integer $k$ such that $x=y^k$ or $y=x^k$. We denote the vertex connectivity of power graph $\mathcal{P}(G)$ by $\mathcal{K}(\mathcal{P}(G))$ and the algebraic connectivity of power graph $\mathcal{P}(G)$ by $\lambda_{n-1}(\mathcal{P}(G))$. This paper investigates the upper bound for the vertex connectivity and the algebraic connectivity of $\mathcal{P}(\mathbb{Z}_{n})$. Moreover, we discuss the equivalent conditions for $\mathcal{P}(\mathbb{Z}_{n})$ to be Laplacian integral. Further the conjecture for an upper bound of the algebraic connectivity of $\mathcal{P}(\mathbb{Z}_{n})$ is posed in this article.
کلیدواژه‌ها
Power graph؛ Algebraic connectivity؛ Vertex connectivity؛ Laplacian integral؛ Finite cyclic group

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