Nilpotent groups whose Difference graphs have positive genus
| Autor: | Parveen, Jitender Kumar |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | The power graph of a finite group $G$ is a simple undirected graph with vertex set $G$ and two vertices are adjacent if one is a power of the other. The enhanced power graph of a finite group $G$ is a simple undirected graph whose vertex set is the group $G$ and two vertices $a$ and $b$ are adjacent if there exists $c \in G$ such that both $a$ and $b$ are powers of $c$. In this paper, we study the difference graph $\mathcal{D}(G)$ of a finite group $G$ which is the difference of the enhanced power graph and the power graph of $G$ with all isolated vertices removed. We characterize all the finite nilpotent groups $G$ such that the genus (or cross-cap) of the difference graph $\mathcal{D}(G)$ is at most $2$. Comment: 13 Figures. arXiv admin note: text overlap with arXiv:2212.07705 |
| Databáze: | arXiv |
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