The concept of Sombor index $\left(SO\right)$ was recently introduced by Gutman in the chemical graph theory. It is a vertex-degree-based topological index and is denoted by Sombor index $SO$: $SO=SO\left(G\right)=\sum _{v_i{v}_j\in E\left(G\right)}\sqrt{d_G{\left(v_i\right)}^2+d_G{\left(v_j\right)}^2},$ where $d_G\left(v_i\right)$ is the degree of vertex $v_i$ in G. Here, we present novel lower and upper bounds on the Sombor index of graphs by using some graph parameters. Moreover, we obtain several relations on Sombor index with the first and second Zagreb indices of graphs. Finally, we give some conclusions and propose future work.

中文翻译：

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轰炸指数

Sombor指数的概念 $（\mathrm{小号}Ø）$是Gutman最近在化学图论中引入的。它是基于顶点度的拓扑索引，用Sombor索引表示$\mathrm{小号}Ø$： $\mathrm{小号}Ø=\mathrm{小号}Ø（G）=\sum _{v_{\mathrm{一世}}{v}_{Ĵ}\in Ë（G）}\sqrt{d_G{（v_{\mathrm{一世}}）}^2+d_G{（v_{Ĵ}）}^2}，$ 哪里 $d_G（v_{\mathrm{一世}}）$ 是顶点的度数 $v_{\mathrm{一世}}$在G中。在这里，我们通过使用一些图参数来呈现图的Sombor索引的新颖上下限。此外，我们获得了图的第一和第二Zagreb指数在Sombor指数上的几种关系。最后，我们给出一些结论并提出未来的工作。