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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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[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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