  Let $G=(V,E)$ be a finite simple graph. The Sombor index $SO(G)$ of $G$ is
defined as $\sum_{uv\in E(G)}\sqrt{d_u^2+d_v^2}$, where $d_u$ is the degree of
vertex $u$ in $G$. In this paper, we study this index for certain graphs and we
examine the effects on $SO(G)$ when $G$ is modified by operations on vertex and
edge of $G$. Also we present bounds for the Sombor index of join and corona
product of two graphs.
