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The general sum-connectivity index χα(G)$\chi_{\alpha}(G)$, for a (molecular) graph G, is defined as the sum of the weights (dG(a1)+dG(a2))α$(d_{G}(a_{1})+d_{G}(a_{2}))^{\alpha}$ of all a1a2∈E(G)$a_{1}a_{2}\in E(G)$, where dG(a1)$d_{G}(a_{1})$ (or dG(a2)$d_{G}(a_{2})$) denotes the degree of a vertex a1$a_{1}$ (or a2$a_{2}$) in the graph G; E(G)$E(G)$ denotes the set of edges of G, and α is an arbitrary real number. Eliasi and Taeri (Discrete Appl. Math. 157:794-803, 2009) introduced four new operations based on the graphs S(G)$S(G)$, R(G)$R(G)$, Q(G)$Q(G)$, and T(G)$T(G)$, and they also computed the Wiener index of these graph operations in terms of W(F(G))$W(F(G))$ and W(H)$W(H)$, where F is one of the symbols S, R, Q, T. The aim of this paper is to obtain sharp bounds on the general sum-connectivity index of the four operations on graphs.

The sharp bounds on general sum-connectivity index of four operations on graphs