The general sum-connectivity index is a molecular descriptor defined as chi_{alpha}(X)=sum_{xyin E(X)}(d_{X}(x)+d_{X}(y))^{alpha}, where d_{X}(x) denotes the degree of a vertex xin X, and α is a real number. Let X be a graph; then let R(X) be the graph obtained from X by adding a new vertex x_{e} corresponding to each edge of X and joining x_{e} to the end vertices of the corresponding edge ein E(X). In this paper we obtain the lower and upper bounds for the general sum-connectivity index of four types of graph operations involving R-graph. Additionally, we determine the bounds for the general sum-connectivity index of line graph L(X) and rooted product of graphs.