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Mohammad Reza Farahani

generalized sum-connectivity index, Appl. Math. Lett., 24, (2010), 402-405 [5] M.R. Farahani, Computing Randic, Geometric-Arithmetic and Atom-Bond Connectivity indices of Circumcoronene Series of Benzenoid, Int. J. Chem. Model., 5 (4), (2013) [6] M.R. Farahani, Some Connectivity Indices and Zagreb Index of Polyhex Nanotubes, Acta Chim. Slov., 59, (2012), 779-783 [7] M.R. Farahani, Third-Connectivity and Third-sum-Connectivity Indices of Circumcoronene Series of Benzenoid Hk, Acta Chim. Slov, 60, (2013), 198

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V.R. Kulli, B. Chaluvaraju and H.S. Boregowda

R eferences [1] K.Ch. Das, S. Das and B. Zhou, Sum-connectivity index of a graph , Front. Math., China 11 (2016) 47–54. doi:10.1007/s11464-015-0470-2 [2] I. Gutman and B. Furtula, Recent Results in the Theory of Randić Index (Univ. Kragujevac, Kragujevac, 2008). [3] I. Gutman and N. Trinajstić, Graph theory and molecular orbitals. Total ϕ-electron energy of alternant hydrocarbons , Chem. Phys. Lett. 17 (1972) 535–538. doi:10.1016/0009-2614(72)85099-1 [4] I. Gutman, V.R. Kulli, B. Chaluvaraju and H.S. Boregowda, On Banhatti and

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V. Lokesha, R. Shruti and T. Deepika

the basis of the vertex-degree of graph one of the vertex-degree based index namely Harmonic index H ( G ) is defined as, H ( G ) = ∑ u v ∈ E ( G ) 2 d u + d v $$\begin{array}{} \displaystyle H(G) = \sum_{uv\in E(G)}\frac{2}{d_u+d_v} \end{array}$$ for more results on Harmonic index we refer to the articles [ 18 , 26 , 28 ]. Randic index: The connectivity index introduced in 1975 by Milan Randic [ 22 ], who has shown this index to reflect molecular branching, Randic index was defined as, R ( G ) = ∑ u v ∈ E ( G ) 1 ( d u . d v ) . $$\begin

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Muhammad Shoaib Sardar, Sohail Zafar and Zohaib Zahid

) [ d u + d v ] . $$\begin{array}{} \displaystyle DD\left( G \right) = \sum\limits_{\{ u,v\} \subseteq V\left( G \right)} {d\left( {u,v} \right)} [{d_u} + {d_v}]. \end{array}$$ Randić index introduced by Milan Randić in 1975 (see [ 30 ]). This index is defined as follows: R ( G ) = ∑ u v ∈ E ( G ) 1 d u d v . $$\begin{array}{} \displaystyle R(G)=\sum\limits_{uv \in E(G)} \frac{1}{\sqrt{d_ud_v}}. \end{array}$$ (5) Later, this index was generalized by Bollobás and Erdös (see [ 4 ]) to the following form for any real number α , and named the general

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Lingping Zhong

R eferences [1] C. Betancur, R. Cruz and J. Rada, Vertex-degree-based topological indices over star-like trees , Discrete Appl. Math. 185 (2015) 18–25. doi:10.1016/j.dam.2014.12.021 [2] H. Deng, S. Balachandran and S.K. Ayyaswamy, On two conjectures of Randić index and the largest signless Laplacian eigenvalue of graphs , J. Math. Anal. Appl. 411 (2014) 196–200. doi:10.1016/j.jmaa.2013.09.014 [3] H. Deng, S. Balachandran, S.K. Ayyaswamy and Y.B. Venkatakrishnan, On the harmonic index and the chromatic number of a graph , Discrete Appl

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Prosanta Sarkar, Nilanjan De and Anita Pal

References 1. Gutman, I.; Trinajstic, N. Graph theory and molecular orbitals total π -electron energy of alternant hydrocarbons. Chem. Phys. Lett. , 1972 , 17 , 535-538. 2. Ranjini, P.S.; Lokesha, V. and Usha, A. Relation between phenylene and hexagonal squeeze using harmonic index. Int. J. Graph Theory. 2013 , 1 , 116-121. 3. Li, X.; Zheng, J.A unified approach to the extremal trees for different indices. MATCH Commun. Math. Comput. Chem. 2005 , 54 , 195-208. 4. Gutman, I.; Lepović, M. Choosing the exponent in the

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Juan Alberto Rodríguez-Velázquez, Erick David Rodríguez-Bazan and Alejandro Estrada-Moreno

R eferences [1] D.W. Bange, A.E. Barkauskas and P.J. Slater, Efficient dominating sets in graphs , in: Appl. Discrete Math., R.D. Ringeisen and F.S. Roberts (Ed(s)), (SIAM, Philadelphia, PA, 1988) 189–199. [2] A. Estrada-Moreno, E.D. Rodríguez-Bazan and J.A. Rodríguez-Velázquez, On the General Randić index of polymeric networks modelled by generalized Sierpiński graphs . arXiv:1510.07982 [math.CO] [3] R. Frucht and F. Harary, On the corona of two graphs , Aequationes Math. 4 (1970) 322–325. doi:10.1007/BF01844162 [4] T. Gallai, Über

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M. P. Vlad and M. V. Diudea

-213. 10. Wiener, H. Structural determination of the paraffin boiling points, J. Am. Chem. Soc. 1947, 69, 17-20. 11. Randić, M. Novel molecular descriptor for structure-property studies. Chem. Phys. Lett. 1993, 211, 478-483. 12. Diudea, M. V.; Hosoya-Diudea polynomials revisited. MATCH Commun. Math.Comput. Chem. 2013, 69, 93-110. 13. Diudea, M. V.; Ashrafi, A. R. Shell-polynomials and Cluj-Tehran index in tori T(4,4)S[5,n]. Acta Chim. Sloven. 2010, 57, 559-564. 14. Ursu, O.; Diudea, M. V. TOPOCLUJ software

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Abaid ur Rehman Virk and Muhammad Quraish

chemical graph theory [ 13 ], [ 14 ]. Another oldest topological index is Randic index introduced by Milan Randic in 1975. The Randic index [ 15 ] is defined as: R − 1 2 ( G ) = ∑ u v ϵ E ( G ) 1 d u d v $$ R_{-\frac{1}{2}}(G)=\sum_{uv\epsilon E(G)}\frac{1}{\sqrt{d_{u}d_{v}}}$$ After some time Ballobas and Erdos [ 16 ] in 1998,and Amic et al. [ 17 ] gives the concept of generalized Randic index. Mathematicians and chemists gain many results from this concept [ 18