On the minimum cut-sets of the power graph of a finite cyclic group
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2022
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916589265223680 |
|---|---|
| author | Mukherjee, Sanjay Patra, Kamal Lochan Sahoo, Binod Kumar |
| author_facet | Mukherjee, Sanjay Patra, Kamal Lochan Sahoo, Binod Kumar |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_13989 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the minimum cut-sets of the power graph of a finite cyclic group Mukherjee, Sanjay Patra, Kamal Lochan Sahoo, Binod Kumar Combinatorics 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. |
| title | On the minimum cut-sets of the power graph of a finite cyclic group |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2209.13989 |