Nirmala and Banhatti-Sombor Index over Tensor and Cartesian Product of Special Class of Semigroup Graphs

Abstract

The Nirmala and first Banhatti-Sombor index which is originated from Sombor index is designated by $N\left(G\right)={\displaystyle {\sum }_{uv\in E\left(G\right)}\sqrt{\left(d_u\right)+\left(d_v\right)}}$ and ${\text{BSO}}_1\left(G\right)={\displaystyle {\sum }_{uv\in E\left(G\right)}\left(1/\sqrt{{\left(d_u\right)}^2+{\left(d_v\right)}^2}\right)}$ , respectively. In this work, we calculated the Nirmala and Banhatti-Sombor index over the tensor and Cartesian product of a graph of an algebraic structure by presenting two different algorithms.