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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.

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