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The sharp bounds on general sum-connectivity index of four operations on graphs. (English) Zbl 1346.05242
Summary: The general sum-connectivity index $$\chi_{\alpha}(G)$$, for a (molecular) graph $$G$$, is defined as the sum of the weights $$(d_{G}(a_{1})+d_{G}(a_{2}))^{\alpha}$$ of all $$a_{1}a_{2}\in E(G)$$, where $$d_{G}(a_{1})$$ (or $$d_{G}(a_{2})$$) denotes the degree of a vertex $$a_{1}$$ (or $$a_{2}$$) in the graph $$G$$; $$E(G)$$ denotes the set of edges of $$G$$, and $$\alpha$$ is an arbitrary real number. M. Eliasi and B. Taeri [Discrete Appl. Math. 157, No. 4, 794–803 (2009; Zbl 1172.05318)] introduced four new operations based on the graphs $$S(G)$$, $$R(G)$$, $$Q(G)$$, and $$T(G)$$, and they also computed the Wiener index of these graph operations in terms of $$W(F(G))$$ and $$W(H)$$, 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.

##### MSC:
 05C76 Graph operations (line graphs, products, etc.) 05C40 Connectivity 05C12 Distance in graphs 05C90 Applications of graph theory
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