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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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##### References:
 [1] Eliasi, M; Taeri, B, Four new sums of graphs and their Wiener indices, Discrete Appl. Math., 157, 794-803, (2009) · Zbl 1172.05318 [2] Gutman, I; Trinajstić, N, Graph theory and molecular orbitals. total $$π$$-electron energy of alternant hydrocarbons, Chem. Phys. Lett., 17, 535-538, (1972) [3] Randić, M, On characterization of molecular branching, J. Am. Chem. Soc., 97, 6609-6615, (1975) · Zbl 0770.60091 [4] Li, X, Gutman, I: Mathematical Aspects of Randić Type Molecular Structure Description. University of Kragujevac, Kragujevac (2006) · Zbl 1294.92032 [5] Zhou, B; Trinajstić, N, On a novel connectivity index, J. Math. Chem., 46, 1252-1270, (2009) · Zbl 1197.92060 [6] Zhou, B; Trinajstić, N, On general sum-connectivity index, J. Math. Chem., 47, 210-218, (2010) · Zbl 1195.92083 [7] Lučić, B; Trinajstić, N; Zhou, B, Comparison between the sum-connectivity index and product-connectivity index for benzenoid hydrocarbons, Chem. Phys. Lett., 475, 146-148, (2009) [8] Akhter, S; Imran, M, On degree based topological descriptors of strong product graphs, Can. J. Chem., 94, 559-565, (2016) [9] Khalifeh, MH; Azari, HY; Ashrafi, AR, The first and second Zagreb indices of some graph operations, Discrete Appl. Math., 157, 804-811, (2009) · Zbl 1172.05314 [10] Zhou, B, Zagreb indices, MATCH Commun. Math. Comput. Chem., 52, 113-118, (2004) · Zbl 1077.05519 [11] Du, Z; Zhou, B; Trinajstić, N, On the general sum-connectivity index of trees, Appl. Math. Lett., 24, 402-405, (2011) · Zbl 1203.05033 [12] Du, Z; Zhou, B; Trinajstić, N, Minimum general sum-connectivity index of unicyclic graphs, J. Math. Chem., 48, 697-703, (2010) · Zbl 1293.05048 [13] Tache, R-M, General sum-connectivity index with $$α≥1$$ for bicyclic graphs, MATCH Commun. Math. Comput. Chem., 72, 761-774, (2014) · Zbl 06704643 [14] Tomescu, I; Kanwal, S, Ordering trees having small general sum-connectivity index, MATCH Commun. Math. Comput. Chem., 69, 535-548, (2013) · Zbl 1299.05040 [15] Tomescu, I; Kanwal, S, Unicyclic graphs of given girth $$k≥4$$ having smallest general sum-connectivity index, Discrete Appl. Math., 164, 344-348, (2014) · Zbl 1321.05141 [16] Tomescu, I, 2-connected graphs with minimum general sum-connectivity index, Discrete Appl. Math., 178, 135-141, (2014) · Zbl 1297.05135 [17] Tomescu, I; Kanwal, S, On the general sum-connectivity index of connnected unicyclic graphs with $$k$$ pendant vertices, Discrete Appl. Math., 181, 306-309, (2015) · Zbl 1304.05087 [18] Deng, H; Sarala, D; Ayyaswamy, SK; Balachandran, S, The Zagreb indices of four operations on graphs, Appl. Math. Comput., 275, 422-431, (2016) · Zbl 1410.05176
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