On Difference of Enhanced Power Graph and Power Graph of a Finite Group
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866909293132906496 |
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| author | Biswas, Sucharita Cameron, Peter J. Das, Angsuman Dey, Hiranya Kishore |
| author_facet | Biswas, Sucharita Cameron, Peter J. Das, Angsuman Dey, Hiranya Kishore |
| contents | The difference graph $D(G)$ of a finite group $G$ is the difference of enhanced power graph of $G$ and power graph of $G$, with all isolated vertices are removed. In this paper we study the connectedness and perfectness of $D(G)$ with respect to various properties of the underlying group $G$. We also find several connection between the difference graph of $G$ and the Gruenberg-Kegel graph of $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_12422 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On Difference of Enhanced Power Graph and Power Graph of a Finite Group Biswas, Sucharita Cameron, Peter J. Das, Angsuman Dey, Hiranya Kishore Combinatorics Group Theory 05C25, 05C17 The difference graph $D(G)$ of a finite group $G$ is the difference of enhanced power graph of $G$ and power graph of $G$, with all isolated vertices are removed. In this paper we study the connectedness and perfectness of $D(G)$ with respect to various properties of the underlying group $G$. We also find several connection between the difference graph of $G$ and the Gruenberg-Kegel graph of $G$. |
| title | On Difference of Enhanced Power Graph and Power Graph of a Finite Group |
| topic | Combinatorics Group Theory 05C25, 05C17 |
| url | https://arxiv.org/abs/2206.12422 |