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arXiv · 2209.13989

On the minimum cut-sets of the power graph of a finite cyclic group

Sanjay Mukherjee·Kamal Lochan Patra·Binod Kumar Sahoo
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Abstract

The power graph $\mathcal{P}(G)$ of a finite group $G$ is the simple graph with vertex set $G$, in which two distinct vertices are adjacent if one of them is a power of the other. For an integer $n\geq 2$, let $C_n$ denote the cyclic group of order $n$ and let $r$ be the number of distinct prime divisors of $n$. The minimum cut-sets of $\mathcal{P}(C_n)$ are characterized in \cite{cps} for $r\leq 3$. In this paper, for $r\geq 4$, we identify certain cut-sets of $\mathcal{P}(C_n)$ such that any minimum cut-set of $\mathcal{P}(C_n)$ must be one of them.

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Sanjay Mukherjee, Kamal Lochan Patra, Binod Kumar Sahoo. 2022-09-28. On the minimum cut-sets of the power graph of a finite cyclic group. https://doi.org/10.1142/s0219498824501767

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