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Journal articles on the topic 'Downhill product connectivity index'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

V.R., Kulli. "Downhill Product Connectivity Indices of Graphs." International Journal of Mathematics and Computer Research 13 (May 21, 2025): 5223–26. https://doi.org/10.5281/zenodo.15481118.

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In this study, we introduce the downhill product connectivity index and reciprocal downhill product connectivity index and their corresponding exponentials of a graph. Furthermore, we compute these indices for some standard graphs, wheel graphs.

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2

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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3

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, multiplic

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4

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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5

V.R.Kulli. "Atom Bond Connectivity Reverse and Product Connectivity Reverse Indices of Oxide and Honeycomb Networks." International Journal of Fuzzy Mathematical Archive 15, no. 01 (2018): 01–05. http://dx.doi.org/10.22457/ijfma.v15n1a1.

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The connectivity indices are applied to measure the chemical characteristics of compounds in Chemical Graph Theory. In this paper, we propose a new index known as the atom bond connectivity reverse index of a molecular graph. Furthermore, we determine the atom bond connectivity reverse index and product connectivity reverse index for oxide and honeycomb networks. Keywords: atom bond connectivity revers

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6

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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7

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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8

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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9

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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10

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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11

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

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12

Boregowda, H. S., B. Chaluvaraju, and V. R. Kulli. "The product connectivity Banhatti index of a graph." Discussiones Mathematicae Graph Theory 39, no. 2 (2019): 505. http://dx.doi.org/10.7151/dmgt.2098.

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13

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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14

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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15

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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16

Kulli, V. R. "Product Connectivity Leap Index and ABC Leap Index of Helm Graphs." Annals of Pure and Applied Mathematics 18, no. 2 (2018): 189–92. http://dx.doi.org/10.22457/apam.v18n2a8.

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17

Tavakoli, M., F. Rahbarnia, and A. R. Ashrafi. "Eccentric Connectivity and Zagreb Coindices of the Generalized Hierarchical Product of Graphs." Journal of Discrete Mathematics 2014 (November 27, 2014): 1–5. http://dx.doi.org/10.1155/2014/292679.

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Formulas for calculations of the eccentric connectivity index and Zagreb coindices of graphs under generalized hierarchical product are presented. As an application, explicit formulas for eccentric connectivity index and Zagreb coindices of some chemical graphs are obtained.

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18

Ramane, Harishchandra S., Vinayak V. Manjalapur, and Ivan Gutman. "General sum-connectivity index, general product-connectivity index, general Zagreb index and coindices of line graph of subdivision graphs." AKCE International Journal of Graphs and Combinatorics 14, no. 1 (2017): 92–100. http://dx.doi.org/10.1016/j.akcej.2017.01.002.

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19

Zhang, Ying-Fang, Muhammad Usman Ghani, Faisal Sultan, Mustafa Inc, and Murat Cancan. "Connecting SiO4 in Silicate and Silicate Chain Networks to Compute Kulli Temperature Indices." Molecules 27, no. 21 (2022): 7533. http://dx.doi.org/10.3390/molecules27217533.

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A topological index is a numerical parameter that is derived mathematically from a graph structure. In chemical graph theory, these indices are used to quantify the chemical properties of chemical compounds. We compute the first and second temperature, hyper temperature indices, the sum connectivity temperature index, the product connectivity temperature index, the reciprocal product connectivity temperature index and the F temperature index of a molecular graph silicate network and silicate chain network. Furthermore, a QSPR study of the key topological indices is provided, and it is demonstr

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20

Basavanagoud, B., and C. S. Gali. "On the General Product-connectivity Index of Transformation Graphs." International Journal of Scientific Research in Mathematical and Statistical Sciences 5, no. 5 (2018): 33–40. http://dx.doi.org/10.26438/ijsrmss/v5i5.3340.

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21

Kulli, V. R. "On the Product Connectivity Revan Index of Certain Nanotubes." Journal of Computer and Mathematical Sciences 8, no. 10 (2017): 562–67. http://dx.doi.org/10.29055/jcms/694.

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22

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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23

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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24

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–arithm

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25

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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26

Wang, Xing-Long, Jia-Bao Liu, Akbar Jahanbani, Muhammad Kamran Siddiqui, Nader Jafari Rad, and Roslan Hasni. "On Generalized Topological Indices of Silicon-Carbon." Journal of Mathematics 2020 (April 8, 2020): 1–21. http://dx.doi.org/10.1155/2020/2128594.

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Let Gbe a graph with n vertices and Γu be the degree of its u-th vertex (Γx is the degree of u). In this article, we compute the generalization of Zagreb index, the generalized Zagreb index, the first and second hyper F-indices, the sum connectivity F-index, and the product connectivity F-index graphs of Si2C3−Ip,q, Si2C3−IIp,q, Si2C3−IIIp,q, and SiC3−IIIp,q.

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27

Wang, Xiaojing, Zhen Lin, and Lianying Miao. "Degree-based topological indices of product graphs." Open Journal of Discrete Applied Mathematics 4, no. 3 (2021): 60–71. http://dx.doi.org/10.30538/psrp-odam2021.0064.

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In this paper, we obtain the quantitative calculation formula of the degree-based topological indices of four standard products for the path and regular graphs, which unify to solve the question on the product of these basic graphs without dealing with it one by one separately. As applications, we give the corresponding calculation formula of the general Randić index, the first general Zagreb index, and the general sum-connectivity index.

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28

Ghalavand, Ali, Shiladhar Pawar, and Nandappa D. Soner. "Leap Eccentric Connectivity Index of Subdivision Graphs." Journal of Mathematics 2022 (September 19, 2022): 1–7. http://dx.doi.org/10.1155/2022/7880336.

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The second degree of a vertex in a simple graph is defined as the number of its second neighbors. The leap eccentric connectivity index of a graph M , L ξ c M , is the sum of the product of the second degree and the eccentricity of every vertex in M . In this paper, some lower and upper bounds of L ξ c S M in terms of the numbers of vertices and edges, diameter, and the first Zagreb and third leap Zagreb indices are obtained. Also, the exact values of L ξ c S M for some well-known graphs are computed.

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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-c

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30

Ashrafi, A. R., M. Ghorbani, and M. A. Hossein-Zadeh. "The Eccentric Connectivity Polynomial of some Graph Operations." Serdica Journal of Computing 5, no. 2 (2011): 101–16. http://dx.doi.org/10.55630/sjc.2011.5.101-116.

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The eccentric connectivity index of a graph G, ξ^C, was proposed by Sharma, Goswami and Madan. It is defined as ξ^C(G) = ∑ u ∈ V(G) degG(u)εG(u), where degG(u) denotes the degree of the vertex x in G and εG(u) = Max{d(u, x) | x ∈ V (G)}. The eccentric connectivity polynomial is a polynomial version of this topological index. In this paper, exact formulas for the eccentric connectivity polynomial of Cartesian product, symmetric difference, disjunction and join of graphs are presented.

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31

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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32

Yang, Chenxu, Meng Ji, Kinkar Chandra Das, and Yaping Mao. "Extreme graphs on the Sombor indices." AIMS Mathematics 7, no. 10 (2022): 19126–46. http://dx.doi.org/10.3934/math.20221050.

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<abstract><p>Gutman proposed the concept of Sombor index. It is defined via the term $ \sqrt{d_F(v_i)^2+d_F(v_j)^2} $, where $ d_F(v_i) $ is the degree of the vertex $ v_i $ in graph $ F $. Also, the reduced Sombor index and the Average Sombor index have been introduced recently, and these topological indices have good predictive potential in mathematical chemistry. In this paper, we determine the extreme molecular graphs with the maximum value of Sombor index and the extremal connected graphs with the maximum (reduced) Sombor index. Some inequalities relations among the chemistry

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33

Devillez, Gauvain, Alain Hertz, Hadrien Mélot, and Pierre Hauweele. "Minimum eccentric connectivity index for graphs with fixed order and fixed number of pendant vertices." Yugoslav Journal of Operations Research 29, no. 2 (2019): 193–202. http://dx.doi.org/10.2298/yjor181115010d.

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The eccentric connectivity index of a connected graph G is the sum over all vertices v of the product dG(v)eG(v), where dG(v) is the degree of v in G and eG(v) is the maximum distance between v and any other vertex of G. We characterize, with a new elegant proof, those graphs which have the smallest eccentric connectivity index among all connected graphs of a given order n. Then, given two integers n and p with p ? n - 1, we characterize those graphs which have the smallest eccentric connectivity index among all connected graphs of order n with p pendant vertices.

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34

Ghan, Muhammad Usman, Faisal Sultan, Shahbaz Ali, Moahmmad Reza Farahani, Murat Cancan, and Mehdi Alaeiyan. "Ghani Mersenne Temperature Indices For Silicate Network and Silicate Chain Network." Archives des Sciences 74, no. 4 (2024): 52–56. http://dx.doi.org/10.62227/as/74408.

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One of chemistry’s most fundamental ideas is the chemical bond. It explains why chemical reactions take place or why atoms are drawn to one another. Several features of chemical compounds in a molecular structure can be identified using the mathematical language offered by several types of topological indices. In actuality, a topological index links the molecular structure of chemical compounds to some of its physical characteristics, such as boiling point and stability energy. Such an index specifies the topology of the structure and is an invariant understructure that maintains mappings. It

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35

De, Nilanjan, Sk Md., and Anita Pal. "Modified Eccentric Connectivity Index and Polynomial of Corona Product of Graphs." International Journal of Computer Applications 132, no. 9 (2015): 1–5. http://dx.doi.org/10.5120/ijca2015907536.

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36

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 d

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Ali, Nasir, Zaeema Kousar, Maimoona Safdar, Fikadu Tesgara Tolasa, and Enoch Suleiman. "Mapping Connectivity Patterns: Degree-Based Topological Indices of Corona Product Graphs." Journal of Applied Mathematics 2023 (November 16, 2023): 1–10. http://dx.doi.org/10.1155/2023/8975497.

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Graph theory (GT) is a mathematical field that involves the study of graphs or diagrams that contain points and lines to represent the representation of mathematical truth in a diagrammatic format. From simple graphs, complex network architectures can be built using graph operations. Topological indices (TI) are graph invariants that correlate the physicochemical and interesting properties of different graphs. TI deal with many properties of molecular structure as well. It is important to compute the TI of complex structures. The corona product (CP) of two graphs G and H gives us a new graph o

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Hayat, Sakander, Azri Arfan, Asad Khan, Haziq Jamil, and Mohammed J. F. Alenazi. "An Optimization Problem for Computing Predictive Potential of General Sum/Product-Connectivity Topological Indices of Physicochemical Properties of Benzenoid Hydrocarbons." Axioms 13, no. 6 (2024): 342. http://dx.doi.org/10.3390/axioms13060342.

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For a graph G=(VG,EG), a degree-based graphical index GId takes the general form GId=∑xy∈EGϕ(dx,dy), where ϕ is a symmetric map and di is the degree of i∈VG. For α∈R, if ϕ=(dxdy)α (resp. ϕ=(dx+dy)α), the index is called the general product-connectivity Rα (resp. general sum-connectivity SCIα) index. In this paper, by formulating an optimization problem, we determine the value(s) of α, for which the linear/multiple correlation coefficient of Rα and SCIα with physicochemical properties of benzenoid hydrocarbons is the strongest. This, in turn, fills some research gaps left by similar studies in

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39

Kanwal, Salma, Mariam Imtiaz, Ayesha Manzoor, Nazeeran Idrees, and Ammara Afzal. "Certain topological indices and polynomials for the semitotal-point graph and line graph of semitotal-point graph for Dutch windmill graph." Indonesian Journal of Combinatorics 3, no. 2 (2020): 63. http://dx.doi.org/10.19184/ijc.2019.3.2.1.

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<p>Dutch windmill graph [1, 2] and denoted by <em>Dnm</em>. Order and size of Dutch windmill graph are (<em>n</em>−1)<em>m</em>+1 and mn respectively. In this paper, we computed certain topological indices and polynomials i.e. Zagreb polynomials, hyper Zagreb, Redefined Zagreb indices, modified first Zagreb, Reduced second Zagreb, Reduced Reciprocal Randi´c, 1st Gourava index, 2nd Gourava index, 1st hyper Gourava index, 2nd hyper Gourava index, Product connectivity Gourava index, Sum connectivity Gourava index, Forgotten index, Forgotten polynomials, &

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40

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 prod

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41

Azari, Mahdieh. "Further results on non-self-centrality measures of graphs." Filomat 32, no. 14 (2018): 5137–48. http://dx.doi.org/10.2298/fil1814137a.

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For indicating the non-self-centrality extent of graphs, two new eccentricity-based measures namely third Zagreb eccentricity index E3(G) and non-self-centrality number N(G) of a connected graph G have recently been introduced as E3(G) = ?uv?E(G)|?G(u)-?G(v)| and N(G) = ? {u,v}?V(G) |?G(u)-?G(v)|, where ?G(u) denotes the eccentricity of a vertex u in G. In this paper, we find relation between the third Zagreb eccentricity index of graphs with some eccentricity-based invariants such as second Zagreb eccentricity index and second eccentric connectivity index. We also give sharp upper and lower b

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DEHGARDI, N., and H. ARAM. "Sharp Bounds on the Augmented Zagreb Index of Graph Operations." Kragujevac Journal of Mathematics 44, no. 4 (2020): 509–22. http://dx.doi.org/10.46793/kgjmat2004.509d.

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Let G be a ﬁnite and simple graph with edge set E(G). The augmented Zagreb index of G is ( ) ∑ dG (u )dG (v) 3 AZI (G ) = ---------------------- , dG (u ) + dG (v) − 2 uv∈E(G ) where dG(u) denotes the degree of a vertex u in G. In this paper, we give some bounds of this index for join, corona, cartesian and composition product of graphs by general sum-connectivity index and general Randić index and compute the sharp amount of that for the regular graphs.

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Alsulami, Samirah, Sabir Hussain, Farkhanda Afzal, Mohammad Reza Farahani, and Deeba Afzal. "Topological Properties of Degree-Based Invariants via M-Polynomial Approach." Journal of Mathematics 2022 (March 16, 2022): 1–8. http://dx.doi.org/10.1155/2022/7120094.

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Chemical graph theory provides a link between molecular properties and a molecular graph. The M-polynomial is emerging as an efficient tool to recover the degree-based topological indices in chemical graph theory. In this work, we give the closed formulas of redefined first and second Zagreb indices, modified first Zagreb index, nano-Zagreb index, second hyper-Zagreb index, Randić index, reciprocal Randić index, first Gourava index, and product connectivity Gourava index via M-polynomial. We also present the M-polynomial of silicate network and then closed formulas of topological indices are a

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Gowtham,, K. J., and M. N. Husin,. "A Study of Families of Bistar and Corona Product of Graph: Reverse Topological Indices." Malaysian Journal of Mathematical Sciences 17, no. 4 (2023): 575–86. http://dx.doi.org/10.47836/mjms.17.4.04.

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In the field of cheminformatics, the amalgamation of graph theory, chemistry, along with technology facilitates the establishment of connections between the structural as well as physiochemical attributes of organic compounds by employing certain valuable graph invariants including the corresponding molecular graph. In this work, we examine reverse topological indices, for instance, the reverse Zagreb index, the reverse arithmetic-geometric, the geometric-arithmetic, the reverse Nirmala indices for the bistar graphs B(n;m) , the reverse sum-connectivity index, the reverse Sombor as well as the

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Kurnia, Rian, Ahmad Muchlas Abrar, Abdul Gazir Syarifudin, Verrel Rievaldo Wijaya, Nur Ain Supu, and Erma Suwastika. "ON PROPERTIES OF PRIME IDEAL GRAPHS OF COMMUTATIVE RINGS." BAREKENG: Jurnal Ilmu Matematika dan Terapan 17, no. 3 (2023): 1463–72. http://dx.doi.org/10.30598/barekengvol17iss3pp1463-1472.

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The prime ideal graph of in a finite commutative ring with unity, denoted by , is a graph with elements of as its vertices and two elements in are adjacent if their product is in . In this paper, we explore some interesting properties of . We determined some properties of such as radius, diameter, degree of vertex, girth, clique number, chromatic number, independence number, and domination number. In addition to these properties, we study dimensions of prime ideal graphs, including metric dimension, local metric dimension, and partition dimension; furthermore, we examined topological indices s

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SUN, YUEFANG. "The (3, l)-Rainbow Edge-Index of Cartesian Product Graphs." Journal of Interconnection Networks 17, no. 03n04 (2017): 1741009. http://dx.doi.org/10.1142/s0219265917410092.

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For a graph G and a vertex subset [Formula: see text] of at least two vertices, an S-tree is a subgraph T of G that is a tree with [Formula: see text]. Two S-trees are said to be edge-disjoint if they have no common edge. Let [Formula: see text] denote the maximum number of edge-disjoint S-trees in G. For an integer K with [Formula: see text], the generalized k-edge-connectivity is defined as [Formula: see text]. An S-tree in an edge-colored graph is rainbow if no two edges of it are assigned the same color. Let [Formula: see text] and l be integers with [Formula: see text], the [Formula: see

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Yan, Qi, Nicolas Gaspard, Hitten P. Zaveri, et al. "The connectivity index: an effective metric for grading epileptogenicity." Journal of Neurosurgery 133, no. 4 (2020): 971–78. http://dx.doi.org/10.3171/2019.4.jns195.

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OBJECTIVEThe aim of this study was to investigate the performance of a metric of functional connectivity to classify and grade the excitability of brain regions based on evoked potentials in response to single-pulse electrical stimulation (SPES).METHODSPatients who underwent 1-Hz frequency stimulation at prospectively selected contacts between 2003 and 2014 at the Yale Comprehensive Epilepsy Center were included. The stimulated contacts were classified as the seizure onset zone (SOZ), highly irritative zone (possibly epileptogenic irritative zone [IZp]), and control contacts not involved in th

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Saniel, Demetria May T., Sales G. Aribe Jr, and Jovelin M. Lapates. "Global Connectivity and Ethnic Fractionalization: New Frontiers of Global Trade Agenda." Pertanika Journal of Social Sciences and Humanities 29, no. 4 (2021): 2113–34. http://dx.doi.org/10.47836/pjssh.29.4.01.

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International trade is an exchange that involves goods and services between countries or international territories, and it signifies a significant share of gross domestic product. Global trading provides opportunities for the country to show its products and services through imports and exports. While this international event gives rise to a world economy, global connectivity and ethnic heterogeneity play a significant role. This paper aims to determine whether the ruggedness of a country supports international trade and global connectivity and whether the ruggedness of ethnic heterogeneity su

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Alam, Sajid Mahboob, Fahd Jarad, Abid Mahboob, Imran Siddique, Taner Altunok, and Muhammad Waheed Rasheed. "A Survey on Generalized Topological Indices for Silicon Carbide Structure." Journal of Chemistry 2022 (June 2, 2022): 1–11. http://dx.doi.org/10.1155/2022/7311404.

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The application of graphs in chemical and molecular structures has exponentially increased during the last few years. Topological indices facilitate the collection of beneficial information and provide an approach to understanding the properties of chemical structure by providing information about algebraic graphs. Let G be a graph with u -vertices and Ω u be the degree of u t h vertex. In this manuscript, we compute Zagreb index (ZI), first, and second, Hyper F-indices and sum and product connectivity of F-index of silicon carbides, namely, SiC4 – I[r, s] and SiC4 – II[r, s].

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Vassiliadis, Chris, and John Mylonakis. "PLANNING A PRODUCT FOR TOURING DESTINATIONS THROUGH THE USE OF SPATIAL MATHEMATICAL ANALYSIS." Tourism and hospitality management 12, no. 2 (2006): 71–82. http://dx.doi.org/10.20867/thm.12.2.6.

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Mathematical models provide spatial analysis to help complex decision-making and can be successfully applied to product planning in tourism. This paper presents a case study, and suggests one process by which planning agencies may evaluate the railway stations in the Northern Greece network. Six geographical points of distinction are identified for promotion based on linear-nearest neighbor analysis and the connectivity index. A functional diagram evaluates each point based on infrastructure, natural and cultural attractions. Finally, these indicators suggest marketing considerations, which ma

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