Sombor index of product of graphs

Articles in Press

Document Type : Original paper

Author

Department of Mathematics, College of Science, Shiraz University, Shiraz, Iran

Abstract

Recently a new vertex-degree based molecular structure descriptor was defined as Sombor index. For a simple graph $G$, the Sombor index of $G$, denoted by $SO(G)$, is defined as $\sum_{uv\in E(G)}\sqrt{d_u^2+d_v^2},$ where $d_v$ is the degree of $v$. In this paper we study the Sombor index of many kinds of product of graphs, such as join of graphs, Cartesian product of graphs, tensor product of graphs, and lexicographic product of graphs. We obtain some formulas for the Sombor index of these product of graphs.

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References

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Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 30 January 2025

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