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Characterizations of algebraic and vertex connectivity of power graph of finite cyclic groups | ||
| Journal of Algebra and Related Topics | ||
| دوره 14، Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024).، تیر 2026، صفحه 191-202 اصل مقاله (182.46 K) | ||
| 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 | ||
| مراجع | ||
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