Article
| Title: | Characterizing finite groups whose enhanced power graphs have universal vertices (English) |
| Author: | Costanzo, David G. |
| Author: | Lewis, Mark L. |
| Author: | Schmidt, Stefano |
| Author: | Tsegaye, Eyob |
| Author: | Udell, Gabe |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 74 |
| Issue: | 2 |
| Year: | 2024 |
| Pages: | 637-645 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $G$ be a finite group and construct a graph $\Delta (G)$ by taking $G\setminus \{1\}$ as the vertex set of $\Delta (G)$ and by drawing an edge between two vertices $x$ and $y$ if $\langle x,y\rangle $ is cyclic. Let $K(G)$ be the set consisting of the universal vertices of $\Delta (G)$ along the identity element. For a solvable group $G$, we present a necessary and sufficient condition for $K(G)$ to be nontrivial. We also develop a connection between $\Delta (G)$ and $K(G)$ when $|G|$ is divisible by two distinct primes and the diameter of $\Delta (G)$ is 2. (English) |
| Keyword: | enhanced power graph |
| Keyword: | universal vertex |
| Keyword: | diameter |
| MSC: | 05C25 |
| MSC: | 20D25 |
| DOI: | 10.21136/CMJ.2024.0065-24 |
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| Date available: | 2024-07-10T14:59:52Z |
| Last updated: | 2024-07-15 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152463 |
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