| Autor: |
Damnjanović, Ivan, Stevanović, Dragan |
| Rok vydání: |
2022 |
| Předmět: |
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| DOI: |
10.48550/arxiv.2211.05559 |
| Popis: |
Recently, Gutman [MATCH Commun. Math. Comput. Chem. 86 (2021) 11-16] defined a new graph invariant which is named the Sombor index $\mathrm{SO}(G)$ of a graph $G$ and is computed via the expression \[ \mathrm{SO}(G) = \sum_{u \sim v} \sqrt{\mathrm{deg}(u)^2 + \mathrm{deg}(v)^2} , \] where $\mathrm{deg}(u)$ represents the degree of the vertex $u$ in $G$ and the summing is performed across all the unordered pairs of adjacent vertices $u$ and $v$. Here we take into consideration the set of all the trees $\mathcal{T}_D$ that have a specified degree sequence $D$ and show that the greedy tree attains the minimum Sombor index on the set $\mathcal{T}_D$. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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