Article
| Title: | Quasi-tree graphs with the minimal Sombor indices (English) |
| Author: | Li, Yibo |
| Author: | Liu, Huiqing |
| Author: | Zhang, Ruiting |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 72 |
| Issue: | 4 |
| Year: | 2022 |
| Pages: | 1227-1238 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | The Sombor index $SO(G)$ of a graph $G$ is the sum of the edge weights $\sqrt {d^2_G(u)+d^2_G(v)}$ of all edges $uv$ of $G$, where $d_G(u)$ denotes the degree of the vertex $u$ in $G$. A connected graph $G = (V ,E)$ is called a quasi-tree if there exists $u\in V (G)$ such that $G-u$ is a tree. Denote $\mathscr {Q}(n,k)=\{G \colon G$ is a quasi-tree graph of order $n$ with $G-u$ being a tree and $d_G(u)=k\}$. We determined the minimum and the second minimum Sombor indices of all quasi-trees in $\mathscr {Q}(n,k)$. Furthermore, we characterized the corresponding extremal graphs, respectively. (English) |
| Keyword: | Sombor index |
| Keyword: | quasi-tree |
| Keyword: | tree |
| MSC: | 05C07 |
| MSC: | 05C09 |
| MSC: | 05C35 |
| idZBL: | Zbl 07655797 |
| idMR: | MR4517610 |
| DOI: | 10.21136/CMJ.2022.0152-22 |
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| Date available: | 2022-11-28T11:45:36Z |
| Last updated: | 2023-04-11 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151144 |
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