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Journal articles on the topic 'Multiplicative sum connectivity index'

Author: Grafiati

Published: 3 June 2025

Last updated: 23 June 2025

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1

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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2

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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3

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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4

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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5

V.R.Kulli. "Some Multiplicative Temperature Indices of HC5C7 [p, q] Nanotubes." International Journal of Fuzzy Mathematical Archive 17, no. 02 (2019): 91–98. http://dx.doi.org/10.22457/206ijfma.v17n2a4.

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In Chemical Science, connectivity indices are applied to measure the chemical characteristics of chemical compounds. In this paper, we compute the multiplicative first and second temperature indices, multiplicative first and second hyper temperature indices, multiplicative sum connectivity temperature index, multiplicative product connectivity temperature index, reciprocal multiplicative product temperature index, general multiplicative first and second temperature indices, multiplicative atom bond connectivity temperature index, multiplicative geometric-arithmetic temperature index, multiplicative arithmetic-geometric temperature index, multiplicative F-temperature index, general multiplicative temperature index of HC5C7[p ,q] nanotubes.

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6

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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7

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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8

V.R.Kulli*. "ON FIFTH MULTIPLICATIVE ZAGREB INDICES OF TETRATHIAFULVALENE AND POPAM DENDRIMERS." INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY 7, no. 3 (2018): 471–79. https://doi.org/10.5281/zenodo.1199388.

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A topological index is a numerical parameter mathematically derived from the graph structure. In this paper, we compute the general fifth multiplicative M-Zagreb indices, fifth multiplicative product connectivity index, fifth multiplicative sum connectivity index, fourth multiplicative atom bond connectivity index and fifth multiplicative geometric-arithmetic index of different chemically interesting dendrimers like tetrathiafulvalene and POPAM dendrimers.

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9

Kulli, V. R. "A New Multiplicative Arithmetic-Geometric Index." International Journal of Fuzzy Mathematical Archive 12, no. 02 (2017): 49–53. http://dx.doi.org/10.22457/ijfma.v12n2a1.

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In this paper, we propose a new topological index: first multiplicative arithmetic geometric index of a molecular graph. A topological index is a numeric quantity from the structural graph of a molecule. In this paper, we compute multiplicative sum connectivity index, multiplicative product connectivity index, multiplicative atom bond connectivity index, multiplicative geometric-arithmetic index for titania nanotubes. Also we compute the multiplicative arithmetic-geometric index for titania nanotubes.

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10

Kulli, V. R. "Multiplicative ABC, GA and AG Neighborhood Dakshayani Indices of Dendrimers." International Journal of Fuzzy Mathematical Archive 17, no. 02 (2019): 77–82. http://dx.doi.org/10.22457/203ijfma.v17n2a2.

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Connectivity indices are applied to measure the chemical characteristics of chemical compounds in Chemical Sciences, Medical Sciences. In this study, we introduce the multiplicative ABC neighborhood Dakshayani index, multiplicative GA neighborhood Dakshayani index and multiplicative AG neighborhood Dakshayani index of a molecular graph. We compute these multiplicative connectivity neighborhood Dakshayani indices of POPAM dendrimers. Also we determine the multiplicative sum connectivity neighborhood Dakshayani index and multiplicative product connectivity neighborhood Dakshayani index of POPAM dendrimers.

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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

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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13

Zhang, Zhiqiang, Haidar Ali, Asim Naseem, Usman Babar, Xiujun Zhang, and Parvez Ali. "On Multiplicative Topological Invariants of Magnesium Iodide Structure." Journal of Mathematics 2022 (May 14, 2022): 1–15. http://dx.doi.org/10.1155/2022/6466585.

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In recent times, the applications of graph theory in molecular and chemical structure research have far exceeded human expectations and have grown exponentially. In this paper, we have determined the multiplicative Zagreb indices, multiplicative hyper-Zagreb indices, multiplicative universal Zagreb indices, sum and product connectivity of multiplicative indices, multiplicative atom-bond connectivity index, and multiplicative geometric-arithmetic index of a famous crystalline structure, magnesium iodide MgI 2 .

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14

Ali, Muhammad Asad, Muhammad Shoaib Sardar, Imran Siddique, and Dalal Alrowaili. "Vertex-Based Topological Indices of Double and Strong Double Graph of Dutch Windmill Graph." Journal of Chemistry 2021 (October 26, 2021): 1–12. http://dx.doi.org/10.1155/2021/7057412.

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A measurement of the molecular topology of graphs is known as a topological index, and several physical and chemical properties such as heat formation, boiling point, vaporization, enthalpy, and entropy are used to characterize them. Graph theory is useful in evaluating the relationship between various topological indices of some graphs derived by applying certain graph operations. Graph operations play an important role in many applications of graph theory because many big graphs can be obtained from small graphs. Here, we discuss two graph operations, i.e., double graph and strong double graph. In this article, we will compute the topological indices such as geometric arithmetic index GA , atom bond connectivity index ABC , forgotten index F , inverse sum indeg index ISI , general inverse sum indeg index ISI α , β , first multiplicative-Zagreb index PM 1 and second multiplicative-Zagreb index PM 2 , fifth geometric arithmetic index GA 5 , fourth atom bond connectivity index ABC 4 of double graph, and strong double graph of Dutch Windmill graph D 3 p .

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15

Khabyah, Ali Al. "Mathematical aspects and topological properties of two chemical networks." AIMS Mathematics 8, no. 2 (2022): 4666–81. http://dx.doi.org/10.3934/math.2023230.

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<abstract><p>Graphs give a mathematical model of molecules, and thery are used extensively in chemical investigation. Strategically selections of graph invariants (formerly called "topological indices" or "molecular descriptors") are used in the mathematical modeling of the physio-chemical, pharmacologic, toxicological, and other aspects of chemical compounds. This paper describes a new technique to compute topological indices of two types of chemical networks. Our research examines the mathematical characteristics of molecular descriptors, particularly those that depend on graph degrees. We derive a compact mathematical analysis and neighborhood multiplicative topological indices for product of graphs ($ \mathcal{L} $) and tetrahedral diamond lattices ($ \Omega $). In this paper, the fifth multiplicative Zagreb index, the general fifth multiplicative Zagreb index, the fifth multiplicative hyper-Zagreb index, the fifth multiplicative product connectivity index, the fifth multiplicative sum connectivity index, the fifth multiplicative geometric-arithmetic index, the fifth multiplicative harmonic index and the fifth multiplicative redefined Zagreb index are determined. The comparison study of these topological indices is also discussed.</p></abstract>

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16

Mahboob, Abid, Sajid Mahboob, Mohammed M. M. Jaradat, Nigait Nigar, and Imran Siddique. "On Some Properties of Multiplicative Topological Indices in Silicon-Carbon." Journal of Mathematics 2021 (November 8, 2021): 1–10. http://dx.doi.org/10.1155/2021/4611199.

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The use of graph theory can be visualized in nanochemistry, computer networks, Google maps, and molecular graph which are common areas to elaborate application of this subject. In nanochemistry, a numeric number (topological index) is used to estimate the biological, physical, and structural properties of chemical compounds that are associated with the chemical graph. In this paper, we compute the first and second multiplicative Zagreb indices ( M 1 G and ( M 1 G )), generalized multiplicative geometric arithmetic index ( GA α II G ), and multiplicative sum connectivity and multiplicative product connectivity indices ( SCII G and PCII G ) of SiC 4 − I m , n and SiC 4 − II m , n .

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17

Khalid, A., N. Kausar, M. Munir, M. Gulistan, M. M. Al-Shamiri, and T. Lamoudan. "Topological Indices of Families of Bistar and Corona Product of Graphs." Journal of Mathematics 2022 (April 26, 2022): 1–8. http://dx.doi.org/10.1155/2022/3567824.

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Topological indices are graph invariants that are used to correlate the physicochemical properties of a chemical compound with its (molecular) graph. In this study, we study certain degree-based topological indices such as Randić index, Zagreb indices, multiplicative Zagreb indices, Narumi–Katayama index, atom-bond connectivity index, augmented Zagreb index, geometric-arithmetic index, harmonic index, and sum-connectivity index for the bistar graphs and the corona product K m o K n ′ , where K n ′ represents the complement of complete graph K n .

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18

Khalid, A., N. Kausar, M. Munir, M. Gulistan, M. M. Al-Shamiri, and T. Lamoudan. "Topological Indices of Families of Bistar and Corona Product of Graphs." Journal of Mathematics 2022 (April 26, 2022): 1–8. http://dx.doi.org/10.1155/2022/3567824.

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Topological indices are graph invariants that are used to correlate the physicochemical properties of a chemical compound with its (molecular) graph. In this study, we study certain degree-based topological indices such as Randić index, Zagreb indices, multiplicative Zagreb indices, Narumi–Katayama index, atom-bond connectivity index, augmented Zagreb index, geometric-arithmetic index, harmonic index, and sum-connectivity index for the bistar graphs and the corona product K m o K n ′ , where K n ′ represents the complement of complete graph K n .

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19

Aftab, Muhammad Haroon, Imran Siddique, Joshua Kiddy K. Asamoah, Hamiden Abd El-Wahed Khalifa, and Muhammad Hussain. "Multiplicative Attributes Derived from Graph Invariants for Saztec4 Diamond." Journal of Mathematics 2022 (September 22, 2022): 1–7. http://dx.doi.org/10.1155/2022/9148581.

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This study consists of developing some closed and updated formulas derived from multiplicative graph invariants such as general Randic index GRI R λ 0 ϰ for λ 0 = ± 1 , ± 1 / 2 , ordinary general geometric-arithmetic (OGA), general version of harmonic index (GHI), sum connectivity index (SI), general sum connectivity index (GSI), 1st and 2nd Gourava and hyper-Gourava indices, (ABC) index, Shegehalli and Kanabur indices, 1st generalised version of Zagreb index (GZI), and forgotten index (FI) for the subdivided Aztec diamond network. Aztec diamond is constructed based on the squares boxes. These square boxes are placed at the centre point and nourish the condition s − 1 / 2 + r − 1 / 2 ≤ n . Furthermore, we put a new vertex of degree-2 at each edge of the small boxes, squares in shapes. A new structure is obtained that has the same properties as its parental graph and is called a subdivided Aztec diamond and symbolised as Saztecn. Subsequently, we compute the multiplicative topological attributes to get some new formulas. For this purpose, a simple, connected, and the finite graph is considered by supposing it Y as the graph of the Saztecn. The order and size have also been discussed in this study and found three different kinds of edges (2, 2), (2, 3), and (2, 4) for computing. The discussion on the networks mentioned above provides us with essential results that can be used in the determination of bio and physio activities and can be interspersed with the molecular compounds and their graphical structures better to understand their physical as well as biological properties.

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20

Azari, Mahdieh. "Further results on Zagreb eccentricity coindices." Discrete Mathematics, Algorithms and Applications 12, no. 06 (2020): 2050075. http://dx.doi.org/10.1142/s1793830920500755.

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The eccentric connectivity index and second Zagreb eccentricity index are well-known graph invariants defined as the sums of contributions dependent on the eccentricities of adjacent vertices over all edges of a connected graph. The coindices of these invariants have recently been proposed by considering analogous contributions from the pairs of non-adjacent vertices. Here, we obtain several lower and upper bounds on the eccentric connectivity coindex and second Zagreb eccentricity coindex in terms of some graph parameters such as order, size, number of non-adjacent vertex pairs, radius, and diameter, and relate these invariants to some well-known graph invariants such as Zagreb indices and coindices, status connectivity indices and coindices, ordinary and multiplicative Zagreb eccentricity indices, Wiener index, degree distance, total eccentricity, eccentric connectivity index, second eccentric connectivity index, and eccentric-distance sum. Moreover, we compute the values of these coindices for two graph constructions, namely, double graphs and extended double graphs.

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21

Hussain, Aftab, Muhammad Numan, Nafisa Naz, Saad Ihsan Butt, Adnan Aslam, and Asfand Fahad. "On Topological Indices for New Classes of Benes Network." Journal of Mathematics 2021 (January 18, 2021): 1–7. http://dx.doi.org/10.1155/2021/6690053.

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Topological indices (TIs) transform a molecular graph into a number. The TIs are a vital tool for quantitative structure activity relationship (QSAR) and quantity structure property relationship (QSPR). In this paper, we constructed two classes of Benes network: horizontal cylindrical Benes network HCB r and vertical cylindrical Benes network obtained by identification of vertices of first rows with last row and first column with last column of Benes network, respectively. We derive analytical close formulas for general Randić connectivity index, general Zagreb, first and the second Zagreb (and multiplicative Zagreb), general sum connectivity, atom-bond connectivity ( VCB r ), and geometric arithmetic ABC index of the two classes of Benes networks. Also, the fourth version of GA and the fifth version of ABC indices are computed for these classes of networks.

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22

Akhter, Shehnaz, and Muhammad Imran. "On degree-based topological descriptors of strong product graphs." Canadian Journal of Chemistry 94, no. 6 (2016): 559–65. http://dx.doi.org/10.1139/cjc-2015-0562.

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Topological descriptors are numerical parameters of a graph that characterize its topology and are usually graph invariant. In a QSAR/QSPR study, physicochemical properties and topological indices such as Randić, atom–bond connectivity, and geometric–arithmetic are used to predict the bioactivity of different chemical compounds. There are certain types of topological descriptors such as degree-based topological indices, distance-based topological indices, counting-related topological indices, etc. Among degree-based topological indices, the so-called atom–bond connectivity and geometric–arithmetic are of vital importance. These topological indices correlate certain physicochemical properties such as boiling point, stability, strain energy, etc., of chemical compounds. In this paper, analytical closed formulas for Zagreb indices, multiplicative Zagreb indices, harmonic index, and sum-connectivity index of the strong product of graphs are determined.

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23

Dustigeer, Ghulam, Haidar Ali, Muhammad Imran Khan, and Yu-Ming Chu. "On multiplicative degree based topological indices for planar octahedron networks." Main Group Metal Chemistry 43, no. 1 (2020): 219–28. http://dx.doi.org/10.1515/mgmc-2020-0026.

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Abstract Chemical graph theory is a branch of graph theory in which a chemical compound is presented with a simple graph called a molecular graph. There are atomic bonds in the chemistry of the chemical atomic graph and edges. The graph is connected when there is at least one connection between its vertices. The number that describes the topology of the graph is called the topological index. Cheminformatics is a new subject which is a combination of chemistry, mathematics and information science. It studies quantitative structure-activity (QSAR) and structure-property (QSPR) relationships that are used to predict the biological activities and properties of chemical compounds. We evaluated the second multiplicative Zagreb index, first and second universal Zagreb indices, first and second hyper Zagreb indices, sum and product connectivity indices for the planar octahedron network, triangular prism network, hex planar octahedron network, and give these indices closed analytical formulas.

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24

Imran, Muhammad, and Shehnaz Akhter. "Degree-based topological indices of double graphs and strong double graphs." Discrete Mathematics, Algorithms and Applications 09, no. 05 (2017): 1750066. http://dx.doi.org/10.1142/s1793830917500665.

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The topological indices are useful tools to the theoretical chemists that are provided by the graph theory. They correlate certain physicochemical properties such as boiling point, strain energy, stability, etc. of chemical compounds. For a graph [Formula: see text], the double graph [Formula: see text] is a graph obtained by taking two copies of graph [Formula: see text] and joining each vertex in one copy with the neighbors of corresponding vertex in another copy and strong double graph SD[Formula: see text] of the graph [Formula: see text] is the graph obtained by taking two copies of the graph [Formula: see text] and joining each vertex [Formula: see text] in one copy with the closed neighborhood of the corresponding vertex in another copy. In this paper, we compute the general sum-connectivity index, general Randi[Formula: see text] index, geometric–arithmetic index, general first Zagreb index, first and second multiplicative Zagreb indices for double graphs and strong double graphs and derive the exact expressions for these degree-base topological indices for double graphs and strong double graphs in terms of corresponding index of original graph [Formula: see text].

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25

S Sunantha and P Gayathri. "Degree Based Multiplicative Connectivity Indices of Nanostructures." Mathematical Journal of Interdisciplinary Sciences 7, no. 2 (2019): 149–55. http://dx.doi.org/10.15415/mjis.2019.72019.

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The Multiplicative topological indices of Phenylenic, Naphatalenic, Anthracene and Tetracenic Nanotubes are calculated. The indices like Multiplicative Zagreb, Multiplicative Hyper-Zagreb, Multiplicative Sum connectivity, Multiplicative product connectivity, General multiplicative Zagreb, Multiplicative ABC and Multiplicative GA indices are expressed as a closed formula for the known values of s, t. The proposed formulae will be very useful for the study of nanostructure in the field of nanotechnology.

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26

Kulli, V. R. "On Multiplicative Minus Indices of Titania Nanotubes." International Journal of Fuzzy Mathematical Archive 16, no. 02 (2018): 75–79. http://dx.doi.org/10.22457/ijfma.v16n1a10.

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In this paper, we introduce the multiplicative minus index, multiplicative modified minus index, multiplicative minus connectivity index, multiplicative reciprocal minus connectivity index and general multiplicative minus index of a graph and compute exact formulas for titania nanotubes.

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27

Kulli, V. R. "Sum Augmented and Multiplicative Sum Augmented Indices of Some Nanostructures." Journal of Mathematics and Informatics 24 (2023): 27–31. http://dx.doi.org/10.22457/jmi.v24a03219.

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We put forward the sum augmented index, multiplicative sum augmented index of a graph. We determine the sum augmented index and the multiplicative sum augmented index for polycyclic aromatic hydrocarbons and jagged rectangle benzenoid systems.

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28

Azari, Mahdieh. "Multiplicative-sum Zagreb index of splice, bridge, and bridge-cycle graphs." Boletim da Sociedade Paranaense de Matemática 39, no. 3 (2021): 189–200. http://dx.doi.org/10.5269/bspm.40503.

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The multiplicative-sum Zagreb index is a graph invariant defined as the product of the sums of the degrees of pairs of adjacent vertices in a graph. In this paper, we compute the multiplicative-sum Zagreb index of some composite graphs such as splice graphs, bridge graphs, and bridge-cycle graphs in terms of the multiplicative-sum Zagreb indices of their components. Then, we apply our results to compute the multiplicative-sum Zagreb index for several classes of chemical graphs and nanostructures.

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29

Alameri, Abdu, Mohammed Alsharafi, Yusuf Zeren, Abdelhafid Modabish, and Mohammed El Marraki. "Degree-Based Topological Indices of the Benzenoid Circumcoronene Series." University of Science and Technology Journal for Engineering and Technology 2, no. 1 (2024): 19–34. http://dx.doi.org/10.59222/ustjet.2.1.2.

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This paper deals with some types of topological indices called valency-based indices or degree-Based Indices. Specifically, Multiplicative Forgotten, Multiplicative Yemen, modified Forgotten, modified Yemen, generalized modified first Zagreb, generalized modified sum connectivity, and generalized modified product connectivity indices of the benzenoid circumcoronene series are computed. Moreover, the formulas of polynomials for all these topological indices were derived.

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30

Xu, Chunlei, Batmend Horoldagva, and Lkhagva Buyantogtokh. "Cactus Graphs with Maximal Multiplicative Sum Zagreb Index." Symmetry 13, no. 5 (2021): 913. http://dx.doi.org/10.3390/sym13050913.

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A connected graph G is said to be a cactus if any two cycles have at most one vertex in common. The multiplicative sum Zagreb index of a graph G is the product of the sum of the degrees of adjacent vertices in G. In this paper, we introduce several graph transformations that are useful tools for the study of the extremal properties of the multiplicative sum Zagreb index. Using these transformations and symmetric structural representations of some cactus graphs, we determine the graphs having maximal multiplicative sum Zagreb index for cactus graphs with the prescribed number of pendant vertices (cut edges). Furthermore, the graphs with maximal multiplicative sum Zagreb index are characterized among all cactus graphs of the given order.

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31

Ali, Akbar, Sadia Noureen, Abdul Moeed, Naveed Iqbal, and Taher S. Hassan. "Fixed-Order Chemical Trees with Given Segments and Their Maximum Multiplicative Sum Zagreb Index." Mathematics 12, no. 8 (2024): 1259. http://dx.doi.org/10.3390/math12081259.

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Topological indices are often used to predict the physicochemical properties of molecules. The multiplicative sum Zagreb index is one of the multiplicative versions of the Zagreb indices, which belong to the class of most-examined topological indices. For a graph G with edge set E={e1,e2,⋯,em}, its multiplicative sum Zagreb index is defined as the product of the numbers D(e1),D(e2),⋯,D(em), where D(ei) is the sum of the degrees of the end vertices of ei. A chemical tree is a tree of maximum degree at most 4. In this research work, graphs possessing the maximum multiplicative sum Zagreb index are determined from the class of chemical trees with a given order and fixed number of segments. The values of the multiplicative sum Zagreb index of the obtained extremal trees are also obtained.

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32

Sun, Xiaoling. "The Multiplicative Sum Zagreb Indices of Graphs with Given Clique Number." Journal of Combinatorial Mathematics and Combinatorial Computing 122, no. 1 (2024): 343–50. http://dx.doi.org/10.61091/jcmcc122-28.

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The multiplicative sum Zagreb index is a modified version of the well-known Zagreb indices. The multiplicative sum Zagreb index of a graph G is the product of the sums of the degrees of pairs of adjacent vertices. The mathematical properties of the multiplicative sum Zagreb index of graphs with given graph parameters deserve further study, as they can be used to detect chemical compounds and study network structures in mathematical chemistry. Therefore, in this paper, the maximal and minimal values of the multiplicative sum Zagreb indices of graphs with a given clique number are presented. Furthermore, the corresponding extremal graphs are characterized.

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33

Azari, Mahdieh. "Multiplicative version of eccentric connectivity index." Discrete Applied Mathematics 310 (March 2022): 32–42. http://dx.doi.org/10.1016/j.dam.2021.12.018.

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34

Matejić, M. M., E. I. Milovanović, and I. Milovanović. "Some remarks on general sum-connectivity coindex." Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informatics and mechanics 12, no. 1 (2020): 29–35. http://dx.doi.org/10.5937/spsunp2001029m.

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Let G = (V,E), V = {v1, v2,..., vn} be a simple connected graph with n vertices, m edges and a sequence of vertex degrees d1 ≥ d2 ≥ ··· ≥ dn > 0, di = d(vi). The general sumconnectivity coindex is defined as Ha(G) = ∑i j (di + dj) a , while multiplicative first Zagreb coindex is defined as P1(G) = ∏i j (di + dj). Here a is an arbitrary real number, and i j denotes that vertices i and j are not adjacent. Some relations between Ha(G) and P1(G) are obtained.

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35

Skrekovski, Riste, Darko Dimitrov, Jiemei Zhong, Hualong Wu, and Wei Gao. "Remarks on Multiplicative Atom-Bond Connectivity Index." IEEE Access 7 (2019): 76806–11. http://dx.doi.org/10.1109/access.2019.2920882.

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36

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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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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Matejić, M. M., E. I. Milovanović, and I. Ž. Milovanović. "On relations between inverse sum indeg index and multiplicative sum Zagreb index." Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informatics and mechanics 9, no. 2 (2017): 193–99. http://dx.doi.org/10.5937/spsunp1702193m.

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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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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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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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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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43

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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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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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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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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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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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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Kwun, Young, Abaid Virk, Waqas Nazeer, M. Rehman, and Shin Kang. "On the Multiplicative Degree-Based Topological Indices of Silicon-Carbon Si2C3-I[p,q] and Si2C3-II[p,q]." Symmetry 10, no. 8 (2018): 320. http://dx.doi.org/10.3390/sym10080320.

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The application of graph theory in chemical and molecular structure research has far exceeded people’s expectations, and it has recently grown exponentially. In the molecular graph, atoms are represented by vertices and bonds by edges. Topological indices help us to predict many physico-chemical properties of the concerned molecular compound. In this article, we compute Generalized first and multiplicative Zagreb indices, the multiplicative version of the atomic bond connectivity index, and the Generalized multiplicative Geometric Arithmetic index for silicon-carbon Si2C3−I[p,q] and Si2C3−II[p,q] second.

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50

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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