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Journal articles on the topic 'Sum connectivity index'

Author: Grafiati

Published: 3 June 2025

Last updated: 6 July 2025

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1

Farahani, Mohammad Reza. "The General Connectivity and General Sum-Connectivity Indices of Nanostructures." International Letters of Chemistry, Physics and Astronomy 44 (January 2015): 73–80. http://dx.doi.org/10.18052/www.scipress.com/ilcpa.44.73.

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Let G be a simple graph with vertex set V(G) and edge set E(G). For ∀νi∈V(G),di denotes the degree of νi in G. The Randić connectivity index of the graph G is defined as [1-3] χ(G)=∑e=v1v2є(G)(d1d2)-1/2. The sum-connectivity index is defined as χ(G)=∑e=v1v2є(G)(d1+d2)-1/2. The sum-connectivity index is a new variant of the famous Randić connectivity index usable in quantitative structure-property relationship and quantitative structure-activity relationship studies. The general m-connectivety and general m-sum connectivity indices of G are defined as mχ(G)=∑e=v1v2...vim+1(1/√(di1di2...dim+1)) and mχ(G)=∑e=v1v2...vim+1(1/√(di1+di2+...+dim+1)) where vi1vi2...vim+1 runs over all paths of length m in G. In this paper, we introduce a closed formula of the third-connectivity index and third-sum-connectivity index of nanostructure "Armchair Polyhex Nanotubes TUAC6[m,n]" (m,n≥1).

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2

Farahani, Mohammad Reza. "The General Connectivity and General Sum-Connectivity Indices of Nanostructures." International Letters of Chemistry, Physics and Astronomy 44 (January 14, 2015): 73–80. http://dx.doi.org/10.56431/p-892ddt.

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Let G be a simple graph with vertex set V(G) and edge set E(G). For ∀νi∈V(G),di denotes the degree of νi in G. The Randić connectivity index of the graph G is defined as [1-3] χ(G)=∑e=v1v2є(G)(d1d2)-1/2. The sum-connectivity index is defined as χ(G)=∑e=v1v2є(G)(d1+d2)-1/2. The sum-connectivity index is a new variant of the famous Randić connectivity index usable in quantitative structure-property relationship and quantitative structure-activity relationship studies. The general m-connectivety and general m-sum connectivity indices of G are defined as mχ(G)=∑e=v1v2...vim+1(1/√(di1di2...dim+1)) and mχ(G)=∑e=v1v2...vim+1(1/√(di1+di2+...+dim+1)) where vi1vi2...vim+1 runs over all paths of length m in G. In this paper, we introduce a closed formula of the third-connectivity index and third-sum-connectivity index of nanostructure "Armchair Polyhex Nanotubes TUAC6[m,n]" (m,n≥1).

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3

V.R.Kulli. "DIFFERENT VERSIONS OF ATOM BOND SUM CONNECTIVITY INDEX." INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY 12, no. 3 (2023): 1–11. https://doi.org/10.5281/zenodo.7722786.

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We introduce some new atom bond sum connectivity indices: second, third and fourth atom bond sum connectivity indices of a graph. In this paper, we compute the atom bond sum connectivity index, the second, third and fourth atom bond sum connectivity indices and neighborhood sum atom bond connectivity index of some important chemical drugs such as chloroquine, hydroxychloroquine and remdesivir.

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4

Wang, Shilin, Zhou Bo, and Nenad Trinajstic. "On the sum-connectivity index." Filomat 25, no. 3 (2011): 29–42. http://dx.doi.org/10.2298/fil1103029w.

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The sum-connectivity index of a simple graph G is defined in mathematical chemistry as R+(G) = ? uv?E(G)(du+dv)?1/2, where E(G) is the edge set of G and du is the degree of vertex u in G. We give a best possible lower bound for the sum-connectivity index of a graph (a triangle-free graph, respectively) with n vertices and minimum degree at least two and characterize the extremal graphs, where n ? 11.

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5

Zhou, Bo, and Nenad Trinajstić. "On general sum-connectivity index." Journal of Mathematical Chemistry 47, no. 1 (2009): 210–18. http://dx.doi.org/10.1007/s10910-009-9542-4.

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6

Phanjoubam, Chinglensana, and Sainkupar Mawiong. "A note on general sum-connectivity index." Proyecciones (Antofagasta) 42, no. 6 (2023): 1537–47. http://dx.doi.org/10.22199/issn.0717-6279-5676.

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For a simple finite graph G, general sum-connectivity index is defined for any real number α as χα(G) = , which generalises both the first Zagreb index and the ordinary sum-connectivity index. In this paper, we present some new bounds for the general sum-connectivity index. We also present relation between general sum-connectivity index and general Randić index.

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7

V.R.Kulli. "DOMINATION ATOM BOND SUM CONNECTIVITY INDICES OF CERTAIN NANOSTRUCTURES." INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY 12, no. 8 (2023): 9–16. https://doi.org/10.5281/zenodo.8310981.

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In this paper, we introduce the domination atom bond sum connectivity index, multiplicative domination atom bond sum connectivity index and domination atom bond sum connectivity exponential of a graph. Also we determine these newly defined domination atom bond sum connectivity indices for some chemical drugs such as chloroquine and hydroxychloroquine.

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8

V.R., Kulli *. "MULTIPLICATIVE PRODUCT CONNECTIVITY AND MULTIPLICATIVE SUM CONNECTIVITY INDICES OF DENDRIMER NANOSTARS." INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY 7, no. 2 (2018): 278–83. https://doi.org/10.5281/zenodo.1173466.

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In Chemical Graph Theory, the connectivity indices are applied to measure the chemical characteristics of compounds. In this paper, we compute the multiplicative product connectivity index and the multiplicative sum connectivity index of three infinite families NS<sub>1</sub>[n], NS<sub>2</sub>[n], NS<sub>3</sub>[n] dendrimer nanostars.   <strong>Mathematics Subject Classification :</strong> 05<em>C</em>05, 05<em>C</em>012, 05<em>C</em>090

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9

Xing, Rundan, Bo Zhou, and Nenad Trinajstić. "Sum-connectivity index of molecular trees." Journal of Mathematical Chemistry 48, no. 3 (2010): 583–91. http://dx.doi.org/10.1007/s10910-010-9693-3.

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10

Das, Kinkar Ch, Sumana Das, and Bo Zhou. "Sum-connectivity index of a graph." Frontiers of Mathematics in China 11, no. 1 (2015): 47–54. http://dx.doi.org/10.1007/s11464-015-0470-2.

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11

Kulli, V. R. "NEIGHBORHOOD SUM ATOM BOND CONNECTIVITY INDICES OF SOME NANOSTAR DENDRIMERS." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 11, no. 02 (2023): 3230–35. http://dx.doi.org/10.47191/ijmcr/v11i2.01.

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In this paper, we introduce the neighborhood sum atom bond connectivity index and the multiplicative neighborhood sum atom bond connectivity index of a graph. Also we compute these indices for certain dendrimers

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12

Pattabiraman, K., and A. Santhakumar. "On Topological Indices of Sudoku Graphs and Titania TiO2 Nanotubes." International Journal of Advanced Research in Computer Science and Software Engineering 7, no. 12 (2017): 96. http://dx.doi.org/10.23956/ijarcsse.v7i12.514.

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In this paper, we obtain the exact formulae for some topological indices such as the general sum-connectivity index, atom-bond connectivity index, geometric arithmetic index, inverse sum indeg index, symmetric division deg index and harmonic polynomial of titania TiO2 Nanotubes and Sudoku graphs.

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13

Kulli, V. R. "Multiplicative Atom Bond Sum Connectivity Index of Certain Nanotubes." Annals of Pure and Applied Mathematics 27, no. 01 (2023): 31–35. http://dx.doi.org/10.22457/apam.v27n1a07904.

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We put forward the multiplicative atom bond sum connectivity index of a graph. We determine the atom bond sum connectivity index and the multiplicative atom bond sum connectivity index for some chemical nanostructures such as armchair polyhex nanotubes, zigzag polyhex nanotubes and carbon nanocone networks.

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14

V.R.Kulli. "NEIGHBORHOOD SUM ATOM BOND CONNECTIVITY INDICES OF SOME NANOSTAR DENDRIMERS." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 11, no. 02 (2023): 3230–35. https://doi.org/10.5281/zenodo.7620328.

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In this paper, we introduce the neighborhood sum atom bond connectivity index and the multiplicative neighborhood sum atom bond connectivity index of a graph. Also we compute these indices for certain dendrimers

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15

Jahanbani, Akbar, and Izudin Redzepovic. "On the generalized abs index of graphs." Filomat 37, no. 30 (2023): 10161–69. http://dx.doi.org/10.2298/fil2330161j.

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The atom-bond sum-connectivity (ABS) index is a recently introduced variant of three earlier much-studied graph-based molecular descriptors: Randic, atom-bond connectivity, and sum-connectivity indices. The general atom-bond sum-connectivity index is defined as ABS?(G)=?uv?E(G) (u+dv?2/du+dv)?, where ? is a real number. In this paper, we present some upper and lower bounds on the general atom-bond sum-connectivity index in terms of graph parameters and other graph indices.

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16

V., R. Kulli, Chaluvaraju B., and V. Asha T. "Multiplicative Product Connectivity and Sum Connectivity Indices of Chemical Structures in Drugs." RESEARCH REVIEW International Journal of Multidisciplinary 4, no. 2 (2019): 949–53. https://doi.org/10.5281/zenodo.2596050.

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In Chemical sciences, the multiplicative connectivity indices are used in the analysis of drug molecular structures which are helpful for chemical and medical scientists to find out the chemical and biological characteristics of drugs. In this paper, we compute the multiplicative product and sum connectivity indices of some important nanostar dendrimers which appeared in nanoscience.

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17

Ma, Feiying, and Hanyuan Deng. "On the sum-connectivity index of cacti." Mathematical and Computer Modelling 54, no. 1-2 (2011): 497–507. http://dx.doi.org/10.1016/j.mcm.2011.02.040.

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18

Lucic, Bono, Ivan Sovic, Jadranko Batista, et al. "The Sum-Connectivity Index - An Additive Variant of the Randic Connectivity Index§." Current Computer Aided-Drug Design 9, no. 2 (2013): 184–94. http://dx.doi.org/10.2174/1573409911309020004.

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19

Lučić, Bono, Nenad Trinajstić, and Bo Zhou. "Comparison between the sum-connectivity index and product-connectivity index for benzenoid hydrocarbons." Chemical Physics Letters 475, no. 1-3 (2009): 146–48. http://dx.doi.org/10.1016/j.cplett.2009.05.022.

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20

V. S., Shigehalli, and Austin Merwin Dsouza. "RELATION BETWEEN GENERAL RANDIC INDEX AND ´ GENERAL SUM CONNECTIVITY INDEX." South East Asian J. of Mathematics and Mathematical Sciences 18, no. 02 (2022): 215–28. http://dx.doi.org/10.56827/seajmms.2022.1802.20.

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The general Randi´c index is the sum of weights of (d(u).d(v))k for every edge uv of a molecular graph G. On the other hand general Sum-Connectivity index is the sum of the weights (d(u) + d(v))k for every edge uv of G, where k is a real number and d(u) is the degree of vertex u. Both families of topological indices are well known and closely related. In fact the correlation coefficient value of these two families of indices for the trees representing the Octane Isomers vary between 0.915 to 0.998. In the recent years these families of indices have been extensively explored and studied. The major research on these indices mostly consists of the application in QSPR/QSAR analysis, computation of these indices for various molecular graphs and bounds of the indices for certain graphs, satisfying certain conditions. The main focus of this paper is a comparative study on these two families of indices for various families of graphs. We find a few algebraic relationships between general Randi´c index and general Sum-connectivity index of certain graphs.

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21

Kulli, V. R. "ATOM BOND CONNECTIVITY E-BANHATTI INDICES." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 11, no. 01 (2023): 3201–8. http://dx.doi.org/10.47191/ijmcr/v11i1.13.

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In this paper, we introduce the atom bond connectivity E-Banhatti index and the sum atom bond connectivity E-Banhatti index of a graph. Also we compute these newly defined atom bond connectivity E-Banhatti indices for wheel graphs, friendship graphs, chain silicate networks, honeycomb networks and nanotubes.

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22

Gowtham, Kalkere Jayanna, and Mohamad Nazri Husin. "Multiplicative Reverse Product Connectivity and Multiplicative Reverse Sum Connectivity of Silicate Network." EDUCATUM Journal of Science, Mathematics and Technology 10, no. 1 (2023): 90–100. http://dx.doi.org/10.37134/ejsmt.vol10.1.10.2023.

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The connectivity indices are helpful to estimate the chemical characteristics of the compounds in chemical graph theory. This report introduces the multiplicative reverse product connectivity index and the multiplicative sum connectivity index of the silicate network. Further, there 2D and 3D graphical representations are plotted.

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23

Akhter, S., and R. Farooq. "Computing bounds for the general sum-connectivity index of some graph operations." Algebra and Discrete Mathematics 29, no. 2 (2020): 147–60. http://dx.doi.org/10.12958/adm281.

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24

Du, Zhibin, Bo Zhou, and Nenad Trinajstić. "Minimum general sum-connectivity index of unicyclic graphs." Journal of Mathematical Chemistry 48, no. 3 (2010): 697–703. http://dx.doi.org/10.1007/s10910-010-9702-6.

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25

Du, Zhibin, Bo Zhou, and Nenad Trinajstić. "On the general sum-connectivity index of trees." Applied Mathematics Letters 24, no. 3 (2011): 402–5. http://dx.doi.org/10.1016/j.aml.2010.10.038.

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26

Albalahi, Abeer M., Zhibin Du, and Akbar Ali. "On the general atom-bond sum-connectivity index." AIMS Mathematics 8, no. 10 (2023): 23771–85. http://dx.doi.org/10.3934/math.20231210.

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<abstract><p>This paper is concerned with a generalization of the atom-bond sum-connectivity (ABS) index, devised recently in [A. Ali, B. Furtula, I. Redžepović, I. Gutman, Atom-bond sum-connectivity index, <italic>J. Math. Chem.</italic>, <bold>60</bold> (2022), 2081-2093]. For a connected graph $ G $ with an order greater than $ 2 $, the general atom-bond sum-connectivity index is represented as $ ABS_\gamma(G) $ and is defined as the sum of the quantities $ (1-2(d_x+d_y)^{-1})^{\gamma} $ over all edges $ xy $ of the graph $ G $, where $ d_x $ and $ d_y $ represent the degrees of the vertices $ x $ and $ y $ of $ G $, respectively, and $ \gamma $ is any real number. For $ -10\le \gamma \le 10 $, the significance of $ ABS_\gamma $ is examined on the data set of octane isomers for predicting six selected physicochemical properties of the mentioned compounds; promising results are obtained when the approximated value of $ \gamma $ belongs to the set $ \{-3, 1, 3\} $. The effect of the addition of an edge between two non-adjacent vertices of a graph under $ ABS_\gamma $ is also investigated. Moreover, the graphs possessing the maximum value of $ ABS_{\gamma} $, with $ \gamma &gt; 0 $, are characterized from the set of all connected graphs of a fixed order and a fixed (ⅰ) vertex connectivity not greater than a given number or (ⅱ) matching number.</p></abstract>

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27

Albalahi, Abeer M., Emina Milovanović, and Akbar Ali. "General Atom-Bond Sum-Connectivity Index of Graphs." Mathematics 11, no. 11 (2023): 2494. http://dx.doi.org/10.3390/math11112494.

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This paper is concerned with the general atom-bond sum-connectivity index ABSγ, which is a generalization of the recently proposed atom-bond sum-connectivity index, where γ is any real number. For a connected graph G with more than two vertices, the number ABSγ(G) is defined as the sum of (1−2(dx+dy)−1)γ over all edges xy of the graph G, where dx and dy represent the degrees of the vertices x and y of G, respectively. For −10≤γ≤10, the significance of ABSγ is examined on the data set of twenty-five benzenoid hydrocarbons for predicting their enthalpy of formation. It is found that the predictive ability of the index ABSγ for the selected property of the considered hydrocarbons is comparable to other existing general indices of this type. The effect of the addition of an edge between two non-adjacent vertices of a graph under ABSγ is also investigated. Furthermore, several extremal results regarding trees, general graphs, and triangle-free graphs of a given number of vertices are proved.

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28

Hussain, Zaryab, and Muhammad Ahsan Binyamin. "On the eccentric atom-bond sum-connectivity index." Open Journal of Discrete Applied Mathematics 7, no. 2 (2024): 11–22. https://doi.org/10.30538/psrp-odam2024.0099.

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The eccentric atom-bond sum-connectivity \(\left(ABSC_{e}\right)\) index of a graph \(G\) is defined as \(ABSC_{e}(G)=\sum\limits_{uv\in E(G)}\sqrt{\frac{e_{u}+e_{v}-2}{e_{u}+e_{v}}}\), where \(e_{u}\) and \(e_{v}\) represent the eccentricities of \(u\) and \(v\) respectively. This work presents precise upper and lower bounds for the \(ABSC_{e}\) index of graphs based on their order, size, diameter, and radius. Moreover, we find the maximum and minimum \(ABSC_{e}\) index of trees based on the specified matching number and the number of pendent vertices.

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29

Yasin H., Mohammed, M. Suresh, and Sourav Mondal. "A Variant of Atom Bond Sum Connectivity Index." Match Communications in Mathematical and in Computer Chemistry 94, no. 3 (2025): 761–82. https://doi.org/10.46793/match94-3.06924.

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30

Sardar, Muhammad Shoaib, Sohail Zafar, and Zohaib Zahid. "Computing topological indices of the line graphs of Banana tree graph and Firecracker graph." Applied Mathematics and Nonlinear Sciences 2, no. 1 (2017): 83–92. http://dx.doi.org/10.21042/amns.2017.1.00007.

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AbstractIn this paper, we compute first Zagreb index (coindex), second Zagreb index (coindex), third Zagreb index, first hyper-Zagreb index, atom-bond connectivity index, fourth atom-bond connectivity index, sum connectivity index, Randić connectivity index, augmented Zagreb index, Sanskruti index, geometric-arithmetic connectivity index and fifth geometric-arithmetic connectivity index of the line graphs of Banana tree graph and Firecracker graph.

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31

Kunz, Milan. "Molecular connectivity indices revisited." Collection of Czechoslovak Chemical Communications 55, no. 3 (1990): 630–33. http://dx.doi.org/10.1135/cccc19900630.

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It is shown that the product νiνj of degrees ν of vertices ij, incident with the edge ij, is the number of paths of length 1, 2, and 3 in which the edge is in the center. The unified connectivity index χm = Σ(νiνj)m, where the sum is made over all edges, with m = 1, is the sum of the number of edges, the Platt number and the polarity number. And it is identical with the half sum of the cube A3 of the adjacency matrix A. The Randić index χ-1/2 of regular graphs does not depend on their connectivity.

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32

Sridhara, G., M. R. Rajesh Kanna, and R. S. Indumathi. "Computation of Topological Indices of Graphene." Journal of Nanomaterials 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/969348.

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33

Azari, Mahdieh, and Nasrin Dehgardi. "Trees with maximum multiplicative connectivity indices." Journal of Interdisciplinary Mathematics 27, no. 7 (2024): 1517–29. https://doi.org/10.47974/jim-1862.

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The product-connectivity (also called Randić connectivity) index, sum-connectivity index and harmonic index are among the best-known and most successful vertex-degreebased topological indices in mathematical chemistry. The multiplicative versions of these graph invariants were proposed by Kulli in 2016. In this paper, we give the maximum values of the multiplicative product-connectivity, multiplicative sum-connectivity and multiplicative harmonic indices within the set of trees with a given order and maximum vertex degree and specify the maximal trees.

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34

Atapour, Maryam. "Sharp Lower Bounds of the Sum-Connectivity Index of Unicyclic Graphs." Journal of Mathematics 2021 (September 2, 2021): 1–6. http://dx.doi.org/10.1155/2021/8391480.

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The sum-connectivity index of a graph G is defined as the sum of weights 1 / d u + d v over all edges u v of G , where d u and d v are the degrees of the vertices u and v in graph G , respectively. In this paper, we give a sharp lower bound on the sum-connectivity index unicyclic graphs of order n ≥ 7 and diameter D G ≥ 5 .

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Ali, Akbar, Ivan Gutman, Izudin Redžepović, Jaya Percival Mazorodze, Abeer M. Albalahi, and Amjad E. Hamza. "On the Difference of Atom-Bond Sum-Connectivity and Atom-Bond-Connectivity Indices." MATCH – Communications in Mathematical and in Computer Chemistry 91, no. 3 (2023): 725–40. http://dx.doi.org/10.46793/match.91-3.725a.

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The atom-bond connectivity (ABC) index is one of the wellinvestigated degree-based topological indices. The atom-bond sumconnectivity (ABS) index is a modified version of the ABC index, which was introduced recently. The primary goal of the present paper is to investigate the difference between the aforementioned two indices, namely ABS − ABC. It is shown that the difference ABS − ABC is positive for all graphs of minimum degree at least 2 as well as for all line graphs of those graphs of order at least 5 that are different from the path and cycle graphs. By means of computer search, the difference ABS − ABC is also calculated for all trees of order at most 15.

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Chen, Hanlin, and Hanyuan Deng. "The inverse sum indeg index of graphs with some given parameters." Discrete Mathematics, Algorithms and Applications 10, no. 01 (2018): 1850006. http://dx.doi.org/10.1142/s1793830918500064.

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Let [Formula: see text] be a simple connected graph. The inverse sum indeg index of [Formula: see text], denoted by [Formula: see text], is defined as the sum of the weights [Formula: see text] of all edges [Formula: see text] of [Formula: see text], where [Formula: see text] denotes the degree of a vertex in [Formula: see text]. In this paper, we derive some bounds for the inverse sum indeg index in terms of some graph parameters, such as vertex (edge) connectivity, chromatic number, vertex bipartiteness, etc. The corresponding extremal graphs are characterized, respectively.

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Hatawi, Batool, and Nabil Aref. "Analysis of the properties of the topological Index using (analysis tools)." Al-Kitab Journal for Pure Sciences 7, no. 2 (2023): 50–61. http://dx.doi.org/10.32441/kjps.07.02.p5.

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Graph G has two sets of information: the vertices, V(G), and the edges, E(G). The definitions for the Connectivity, Geometric Arithmetic, Atomic Bond, and Sum Connectivity Indices of G:  were deg(u), deg(v) are a degree of vertices. Dendrimers are synthetic, man-made molecules that are composed of monomers organized in a branching structure. in this article, we calculate Connectivity, Geometric Arithmetic, Atom Bond Connectivity, and Sum Connectivity Index for the PAMAM, POPAM, and HACN1J dendrimers.

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Deng, Fei, Xiujun Zhang, Mehdi Alaeiyan, Abid Mehboob, and Mohammad Reza Farahani. "Topological Indices of the Pent-Heptagonal Nanosheets VC5C7 and HC5C7." Advances in Materials Science and Engineering 2019 (June 23, 2019): 1–12. http://dx.doi.org/10.1155/2019/9594549.

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In this paper, we computed the topological indices of pent-heptagonal nanosheet. Formulas for atom-bond connectivity index, fourth atom-bond connectivity index, Randić connectivity index, sum-connectivity index, first Zagreb index, second Zagreb index, augmented Zagreb index, modified Zagreb index, hyper Zagreb index, geometric-arithmetic index, fifth geometric-arithmetic index, Sanskruti index, forgotten index, and harmonic index of pent-heptagonal nanosheet have been derived.

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39

Chen, Deqiang. "Comparison Between Two Kinds of Connectivity Indices for Measuring the π-Electronic Energies of Benzenoid Hydrocarbons". Zeitschrift für Naturforschung A 74, № 5 (2019): 367–70. http://dx.doi.org/10.1515/zna-2018-0429.

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AbstractIn this paper, we show that both the general product-connectivity index χα and the general sum-connectivity index \({}^{s}{\chi_{\alpha}}\) are closely related molecular descriptors when the real number α is in some interval. By comparing these two kinds of indices, we show that the sum-connectivity index \({}^{s}{\chi_{-0.5601}}\) is the best one for measuring the π-electronic energies of lower benzenoid hydrocarbons. These improve the earlier results.

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40

Awais, M. "General ( α , 2 ) Path Sum Connectivity Index of Nanostructures". Journal of Corrosion and Materials 49, № 1 (2024): 24–28. http://dx.doi.org/10.61336/jcm2024-3.

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The general path sum connectivity index of a molecular graph, denoted as t χ α ( G ) , is defined for a graph G , where α is a positive real number and t is a positive integer. This index is expressed as: t χ α ( G ) = ∑ p t = v j 1 v j 2 … v j t + 1 ⊆ G [ d G ( v j 1 ) + d G ( v j 2 ) + ⋯ + d G ( v j t + 1 ) ] α , where p t represents a path of length t within the graph. In this work, we compute the general path sum connectivity index for various nanostructures, including phenylene, naphthalene, anthracene, and tetracene nanotubes. This index is particularly useful in investigating the physico-chemical properties of chemical compounds and plays a crucial role in the analysis of three-dimensional quantitative structure-activity relationships (3D-QSAR) and molecular chirality.

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41

Zhu, Zhongxun, and Hongyan Lu. "On the general sum-connectivity index of tricyclic graphs." Journal of Applied Mathematics and Computing 51, no. 1-2 (2015): 177–88. http://dx.doi.org/10.1007/s12190-015-0898-2.

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42

Tomescu, Ioan. "2-Connected graphs with minimum general sum-connectivity index." Discrete Applied Mathematics 178 (December 2014): 135–41. http://dx.doi.org/10.1016/j.dam.2014.06.023.

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43

Ali, Akbar, Igor Ž. Milovanović, Emina I. Milovanović, and M. Matejić. "Sharp inequalities for the atom-bond (sum) connectivity index." Journal of Mathematical Inequalities, no. 4 (2023): 1411–26. http://dx.doi.org/10.7153/jmi-2023-17-92.

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44

Imran, Muhammad, Abdul Qudair Baig, Hafiz Muhammad Afzal Siddiqui, and Rabia Sarwar. "On molecular topological properties of diamond-like networks." Canadian Journal of Chemistry 95, no. 7 (2017): 758–70. http://dx.doi.org/10.1139/cjc-2017-0206.

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The Randić (product) connectivity index and its derivative called the sum-connectivity index are well-known topological indices and both of these descriptors correlate well among themselves and with the π-electronic energies of benzenoid hydrocarbons. The general n connectivity of a molecular graph G is defined as [Formula: see text] and the n sum connectivity of a molecular graph G is defined as [Formula: see text], where the paths of length n in G are denoted by [Formula: see text] and the degree of each vertex vi is denoted by di. In this paper, we discuss third connectivity and third sum-connectivity indices of diamond-like networks and compute analytical closed results of these indices for diamond-like networks.

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45

Azari, Mahdieh, and Nasrin Dehgardi. "On trees with maximum exponential harmonic and sum-connectivity indices}." Mathematical Reports 27(77), no. 1-2 (2025): 37–45. https://doi.org/10.59277/mrar.2025.27.77.1.2.37.

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The harmonic index and sum-connectivity index are two of the best-known and most successful vertex-degree-based topological indices in mathematical chemistry. They are well correlated with the $\pi$-electronic energy of benzenoid hydrocarbons. The idea of introducing the exponential of vertex-degree-based topological indices was raised by Rada during the study of discrimination ability of these class of graph invariants. The aim of this research is to study the exponential of harmonic and sum-connectivity index over trees with fixed order and given maximum vertex degree.

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46

Zuo, Xuewu, Jia-Bao Liu, Hifza Iqbal, Kashif Ali, and Syed Tahir Raza Rizvi. "Topological Indices of Certain Transformed Chemical Structures." Journal of Chemistry 2020 (April 15, 2020): 1–7. http://dx.doi.org/10.1155/2020/3045646.

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Topological indices like generalized Randić index, augmented Zagreb index, geometric arithmetic index, harmonic index, product connectivity index, general sum-connectivity index, and atom-bond connectivity index are employed to calculate the bioactivity of chemicals. In this paper, we define these indices for the line graph of k-subdivided linear [n] Tetracene, fullerene networks, tetracenic nanotori, and carbon nanotube networks.

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47

Sigarreta, José M. "Mathematical Properties of Variable Topological Indices." Symmetry 13, no. 1 (2020): 43. http://dx.doi.org/10.3390/sym13010043.

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A topic of current interest in the study of topological indices is to find relations between some index and one or several relevant parameters and/or other indices. In this paper we study two general topological indices Aα and Bα, defined for each graph H=(V(H),E(H)) by Aα(H)=∑ij∈E(H)f(di,dj)α and Bα(H)=∑i∈V(H)h(di)α, where di denotes the degree of the vertex i and α is any real number. Many important topological indices can be obtained from Aα and Bα by choosing appropriate symmetric functions and values of α. This new framework provides new tools that allow to obtain in a unified way inequalities involving many different topological indices. In particular, we obtain new optimal bounds on the variable Zagreb indices, the variable sum-connectivity index, the variable geometric-arithmetic index and the variable inverse sum indeg index. Thus, our approach provides both new tools for the study of topological indices and new bounds for a large class of topological indices. We obtain several optimal bounds of Aα (respectively, Bα) involving Aβ (respectively, Bβ). Moreover, we provide several bounds of the variable geometric-arithmetic index in terms of the variable inverse sum indeg index, and two bounds of the variable inverse sum indeg index in terms of the variable second Zagreb and the variable sum-connectivity indices.

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48

Akhter, Shehnaz, and Muhammad Imran. "On molecular topological properties of benzenoid structures." Canadian Journal of Chemistry 94, no. 8 (2016): 687–98. http://dx.doi.org/10.1139/cjc-2016-0032.

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The degree-based topological indices correlate certain physicochemical properties such as boiling point, strain energy, and stability, etc., of certain chemical compounds. Among the major classes of topological indices are the distance-based topological indices, degree-based topological indices, and counting-related polynomials and corresponding indices of graphs. Among all of the degree-based indices, namely the first general Zagreb index, general Rndić connectivity index, general sum-connectivity index, atom–bond connectivity index (ABC), and geometric–arithmetic index (GA), are most important due to their chemical significance. In this paper, we compute the first general Zagreb index, general Randić connectivity index, general sum-connectivity index, ABC, GA, ABC4, and GA5 indices of hexagonal parallelogram P(m,n) nanotubes, triangular benzenoid Gn, and zigzag-edge coronoid fused with starphene ZCS(k,l,m) nanotubes by using the line graphs of the subdivision of these chemical graphs.

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49

G. Mirajkar, Keerthi, and Pooja B. "Computing Certain Degree Based Topological Indices and Coindices of E-graphs." International Journal of Fuzzy Mathematical Archive 12, no. 02 (2017): 67–73. http://dx.doi.org/10.22457/ijfma.v12n2a3.

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In this paper, we obtain the explicit formulae for general sum-connectivity index, general product-connectivity index, general Zagreb index and coindices of G-networks, extended G-networks and -networks.

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50

Dr., Latha Devi Puli. "Topological indices of Derived graphs of Bull Graph." 'Journal of Research & Development' 15, no. 11 (2023): 131–34. https://doi.org/10.5281/zenodo.8046228.

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A topological index is a numeric number that helps to find the characteristics of  compounds. There are many applications of graph theory. In this paper we compute first and second Zagreb indices, Randi´c index, sum-connectivity index, harmonic index, inverse sum indeg index, modified first and second Zagreb indices and first and second hyper Zagreb indices of the Splitting graph of Bull graph. <strong>2020 Mathematics Subject Classifications</strong>: 05C50, 05C09

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