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.
Visave, C. V. and Deore, R. P. (2025). Characterizations of algebraic and vertex connectivity of power graph of finite cyclic groups. Journal of Algebra and Related Topics, (), -. doi: 10.22124/jart.2025.28572.1719
MLA
Visave, C. V., and Deore, R. P.. "Characterizations of algebraic and vertex connectivity of power graph of finite cyclic groups", Journal of Algebra and Related Topics, , , 2025, -. doi: 10.22124/jart.2025.28572.1719
HARVARD
Visave, C. V., Deore, R. P. (2025). 'Characterizations of algebraic and vertex connectivity of power graph of finite cyclic groups', Journal of Algebra and Related Topics, (), pp. -. doi: 10.22124/jart.2025.28572.1719
CHICAGO
C. V. Visave and R. P. Deore, "Characterizations of algebraic and vertex connectivity of power graph of finite cyclic groups," Journal of Algebra and Related Topics, (2025): -, doi: 10.22124/jart.2025.28572.1719
VANCOUVER
Visave, C. V., Deore, R. P. Characterizations of algebraic and vertex connectivity of power graph of finite cyclic groups. Journal of Algebra and Related Topics, 2025; (): -. doi: 10.22124/jart.2025.28572.1719
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