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Journal articles on the topic 'Randic index'

Author: Grafiati

Published: 5 June 2025

Last updated: 1 August 2025

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1

Litta, Dr E. "Proper Colorings in R-Regular Randic Index Graphs." International Journal for Research in Applied Science and Engineering Technology 12, no. 2 (2024): 1603–7. http://dx.doi.org/10.22214/ijraset.2024.58636.

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Abstract: The new idea of proper colourings in the r-regular Randic index graph has been proposed in this paper. New Chromatic number inequalities connected to the Randic index are established in this paper.

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2

Li, Yingfang, Li Yan, Muhammad Kamran Jamil, Mohammad Reza Farahani, Wei Gao, and Jia-Bao Liu. "Four New/Old Vertex-Degree-Based Topological Indices of HAC5C7[p, q] and HAC5C6C7[p, q] Nanotubes." Journal of Computational and Theoretical Nanoscience 14, no. 1 (2017): 796–99. http://dx.doi.org/10.1166/jctn.2017.6275.

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Recently, Gutman et al. presented some vertex-degree based topological indices, that earlier have been considered in the chemical and/or mathematical literature, but, evaded the attention of most mathematical chemists. These are the reciprocal Randic index (RR), the reduced reciprocal Randic index (RRR), the reduced second Zagreb index (RM2) and the forgotten index (F). In this paper, we compute these topological indices of HAC5C7[p, q] and HAC5C6C7[p, q] nanotubes.

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3

Saleem, Hafsa, Mohamad Nazri Husin, Shahbaz Ali, Muhammad Shazib Hameed, and Zaheer Ahmad. "Topology of Edge Contracted Möbius Ladder: Indices and Dimension." Malaysian Journal of Fundamental and Applied Sciences 20, no. 4 (2024): 739–58. http://dx.doi.org/10.11113/mjfas.v20n4.3386.

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Assigning numbers to graphs serves as a fundamental tool in graph theory and enables various analytical, computational, and visualization techniques for studying and understanding graph structures and properties. Edge Contraction is a process that separates edges from the graph while also joining the two previously linked vertices. In this paper, we study metric dimension and degree-based topological indices of Möbius Ladder and edge contracted Möbius Ladder like first Zagreb index, second Zagreb index, first Zagreb Hyper index, second Zagreb Hyper index, Augmented Zagreb index, Randic index,

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Husin, Nor, Roslan Hasni, Zhibin Du, and Akbar Ali. "More results on extremum Randic indices of (molecular) trees." Filomat 32, no. 10 (2018): 3581–90. http://dx.doi.org/10.2298/fil1810581h.

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The Randic index R(G) of a graph G is the sum of the weights (dudv)-1/2 of all edges uv in G, where du denotes the degree of vertex u. Du and Zhou [On Randic indices of trees, unicyclic graphs, and bicyclic graphs, Int. J. Quantum Chem. 111 (2011), 2760-2770] determined the n-vertex trees with the third for n ? 7, the fourth for n ? 10, the fifth and the sixth for n ? 11 maximum Randic indices. Recently, Li et al. [The Randic indices of trees, unicyclic graphs and bicyclic graphs, Ars Comb. 127 (2016), 409-419] obtained the n-vertex trees with the seventh, the eighth, the ninth and the tenth f

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5

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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6

Agustin, Ika Hesti, A. S. Maragadam, Dafik, V. Lokesha, and M. Manjunath. "Semi-Total Point Graph of Neighbourhood Edge Corona Graph of G and H." European Journal of Pure and Applied Mathematics 16, no. 2 (2023): 1094–109. http://dx.doi.org/10.29020/nybg.ejpam.v16i2.4513.

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A topological index is a function having a set of graphs as its domain and a set of real numbers as its range. Here we concentrated on topological indices involving the number of vertices, the number of edges and the maximum and minimum vertex degree. The aim of this paper is to compute the lower and upper bounds of the second Zagreb index, third Zagreb index, Hyper Zagreb index, Harmonic index, Redefined first Zagreb index, First reformulated Zagreb index, Forgotten topological index, square F-index, Sum-connectivity index, Randic index, Reciprocal Randic index, Gourava index, Sombar index, N

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7

Das, Kinkar, Selvaraj Balachandran, and Ivan Gutman. "Inverse degree, Randic index and harmonic index of graphs." Applicable Analysis and Discrete Mathematics 11, no. 2 (2017): 304–13. http://dx.doi.org/10.2298/aadm1702304d.

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Let G be a graph with vertex set V and edge set E. Let di be the degree of the vertex vi of G. The inverse degree, Randic index, and harmonic index of G are defined as ID = ?vi?V 1/di, R = ? vivj?E 1/?di dj , and H = ? vivj?E 2=(di + dj), respectively. We obtain relations between ID and R as well as between ID and H. Moreover, we prove that in the case of trees, ID > R and ID > H.

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8

Tomescu, Ioan, Misbah Arshad, and Muhammad Jamil. "Extremal topological indices for graphs of given connectivity." Filomat 29, no. 7 (2015): 1639–43. http://dx.doi.org/10.2298/fil1507639t.

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In this paper, we show that in the class of graphs of order n and given (vertex or edge) connectivity equal to k (or at most equal to k), 1 ? k ? n - 1, the graph Kk + (K1? Kn-k-1) is the unique graph such that zeroth-order general Randic index, general sum-connectivity index and general Randic connectivity index are maximum and general hyper-Wiener index is minimum provided ? > 1. Also, for 2-connected (or 2-edge connected) graphs and ? > 0 the unique graph minimizing these indices is the n-vertex cycle Cn.

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9

Arizmendi, Gerardo, and Octavio Arizmendi. "Energy of a graph and Randic index." Linear Algebra and its Applications 609 (January 2021): 332–38. http://dx.doi.org/10.1016/j.laa.2020.09.025.

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10

Mahsa, Hemmasi, and Iranmanesh Ali. "Some bounds on the modified Randic index." Kragujevac Journal of Science, no. 37 (2015): 79–90. http://dx.doi.org/10.5937/kgjsci1537079m.

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11

De Meo, Pasquale, Fabrizio Messina, Domenico Rosaci, Giuseppe M. L. Sarne, and Athanasios V. Vasilakos. "Estimating Graph Robustness Through the Randic Index." IEEE Transactions on Cybernetics 48, no. 11 (2018): 3232–42. http://dx.doi.org/10.1109/tcyb.2017.2763578.

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12

Yu, Fei, Hifza Iqbal, Saira Munir, and Jiabao Liu. "M-polynomial and topological indices of some transformed networks." AIMS Mathematics 6, no. 12 (2021): 13887–906. http://dx.doi.org/10.3934/math.2021804.

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<abstract><p>In the chemical industry, topological indices play an important role in defining the properties of chemical compounds. They are numerical parameters and structure invariant. It is a proven fact by scientists that topological properties are influential tools for interconnection networks. In this paper, we will use stellation, medial and bounded dual operations to build transformed networks from zigzag and triangular benzenoid structures. Using M-polynomial, we compute the first and second Zagreb indices, second modified Zagreb indices, symmetric division index, general

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13

BERINDE, ZOITA-MARIOARA. "Comparing the molecular graph degeneracy of Wiener, Harary, Balaban, Randi´c and ZEP topological indices." Creative Mathematics and Informatics 23, no. 2 (2014): 165–74. http://dx.doi.org/10.37193/cmi.2014.02.02.

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The aim of this paper is to show that the ZEP topological index has better discrimination power than four well known topological indices in molecular chemistry: Balaban index, Harary index, Randic index, and Wiener index.

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14

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 ma

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15

Shanmukha, M. C., A. Usha, M. K. Siddiqui, Samuel Asefa Fufa, and B. M. Praveen. "Degree-Based Molecular Descriptors of Guar Gum and Its Chemical Derivatives." Journal of Chemistry 2022 (February 7, 2022): 1–14. http://dx.doi.org/10.1155/2022/7371538.

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The most abundant polycarbonates that are found in food are polysaccharides. A long chain of monosaccharide with glycosidic linkages forms polymeric carbohydrates. These carbohydrates with water in the process of hydrolysis produces sugar monosaccharides or oligosaccharides. The examples of polysaccharides include starch, galactogen, and glycogen. They contribute various applications mainly in food storage, pharmaceutical industry, and petroleum extraction. In this work, a polysaccharide known as guar gum is studied and also ten degree-based topological indices, namely, Zagreb indices, Randic

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16

Matejic, Marjan, Igor Milovanovic, and Emina Milovanovic. "Some remarks on the general zeroth-order Randic coindex." Filomat 36, no. 6 (2022): 2083–90. http://dx.doi.org/10.2298/fil2206083m.

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Let G = (V, E), V = {v1, v2,..., vn}, be a simple connected graph of order n and size m, without isolated vertices. Denote by d1 ? d2 ?... ? dn, di = d(vi) a sequence of vertex degrees of G. The general zeroth-order Randic index is defined as 0R?(G) = ?ni =1 d?i, where ? is an arbitrary real number. The corresponding general zeroth-order Randic coindex is defined via 0R??(G) = ?ni=1(n?1?di)d?i. Some new bounds for the general zeroth-order Randic coindex and relationship between 0R??(G?) and 0R???1(G?) are obtained. For a particular values of parameter ? a number of new bounds for different top

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17

Milosevic, Predrag, Igor Milovanovic, Emina Milovanovic, and Marjan Matejic. "Some inequalities for general zeroth-order Randic index." Filomat 33, no. 16 (2019): 5249–58. http://dx.doi.org/10.2298/fil1916249m.

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Let G=(V,E), V={v1, v2,..., vn}, be a simple connected graph with n vertices, m edges and vertex degree sequence ? = d1?d2 ?...? dn = ? > 0, di = d(vi). General zeroth-order Randic index of G is defined as 0R?(G) = ?ni =1 d?i , where ? is an arbitrary real number. In this paper we establish relationships between 0R?(G) and 0R?-1(G) and obtain new bounds for 0R?(G). Also, we determine relationship between 0R?(G), 0R?(G) and 0R2?-?(G), where ? and ? are arbitrary real numbers. By the appropriate choice of parameters ? and ?, a number of old/new inequalities for different vertex-degree-based t

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18

Rehman Virik, Abaid ur, and Iqra Malik. "Analysis of COVID-19 by Means of Graph Theory." Scientific Inquiry and Review 4, no. 2 (2020): 48–62. http://dx.doi.org/10.32350/sir.42.04.

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As a powerful displaying, investigation and computational device, graph theory is widely used in biological mathematics to deal with various biology problems. In the field of microbiology, graphs can communicate the sub-atomic structure. Where cell, quality or protein can be indicated as a vertex, and the associate component can be viewed as an edge. Thusly, the biological activity characteristic can be measured via topological index computing in the comparing graphs. In this article, we for the most part concentrate some topological lists for the Corona virus graph. At first,we give a general

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19

Sultana, Sobia. "Prioritizing Asthma Treatment Drugs through Multicriteria Decision Making." International Journal of Analytical Chemistry 2024 (February 5, 2024): 1–10. http://dx.doi.org/10.1155/2024/6516976.

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Asthma is a medical condition characterized by inflammation, narrowing, and swelling of a person’s airways, leading to increased mucus production and difficulties in breathing. Topological indices are instrumental in assessing the physical and chemical attributes of these asthma drugs. As resistance to current treatments continues to emerge and undesirable side effects are linked to certain medications, the search for novel and enhanced drugs becomes a top priority. In this study, the examination of 19 distinct asthma medications was focused. In this study, quantitative structure-activity rela

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20

Elumalai, Suresh, Sunilkumar Hosamani, Toufik Mansour, and Mohammad Rostami. "More on inverse degree and topological indices of graphs." Filomat 32, no. 1 (2018): 165–78. http://dx.doi.org/10.2298/fil1801165e.

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The inverse degree of a graph G with no isolated vertices is defined as the sum of reciprocal of vertex degrees of the graph G. In this paper, we obtain several lower and upper bounds on inverse degree ID(G). Moreover, using computational results, we prove our upper bound is strong and has the smallest deviation from the inverse degree ID(G). Next, we compare inverse degree ID(G) with topological indices (Randic index R(G), geometric-arithmetic index GA(G)) for chemical trees and also we determine the n-vertex chemical trees with the minimum, the second and the third minimum, as well as the se

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21

Deng, Hanyuan, Zikai Tang, and Jie Zhang. "On a conjecture of Randic index and graph radius." Filomat 29, no. 6 (2015): 1369–75. http://dx.doi.org/10.2298/fil1506369d.

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22

Matejic, Marjan, Şerife Altındağ, Emina Milovanovic, and Igor Milovanovic. "On the bounds of zeroth-order general Randic index." Filomat 36, no. 19 (2022): 6443–56. http://dx.doi.org/10.2298/fil2219443m.

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The zeroth-order general Randic index, 0R?(G), of a connected graph G, is defined as 0 P R?(G) = ni =1 d?i , where di is the degree of the vertex vi of G and ? arbitrary real number. We consider linear combinations of the 0R?(G) of the form 0R?(G) ? (? + ?)0R??1(G) + ?? 0R??2(G) and 0R?(G) ? 2a 0R??1(G) + a2 0R??2(G), where a is an arbitrary real number, and determine their bounds. As corollaries, various upper and lower bounds of 0R?(G) and indices that represent some special cases of 0R?(G) are obtained.

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23

Nagarajan, S., and M. Durga. "A Computational Approach on Fenofibrate Drug Using Degree-Based Topological Indices and M-polynomials." Asian Journal of Chemical Sciences 14, no. 2 (2024): 43–57. http://dx.doi.org/10.9734/ajocs/2024/v14i2293.

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Fenofibrate is a drug approved by FDA Food and Drugs Administration used to treat patients with Hypertrigly ceridemia primary hypercholesterolemia or mixed dyslipidemia. It reduces low-density lipoprotein cholesterol (LDL-c), total cholesterol, triglycerides, and apolipoprotein B and increases high -density lipoprotein cholesterol (HDL-C) in adults. The sum and multiplicative versions of several topological indices such as General Zagreb, General Randic, Arithmetic Geometric Index, Inverse sum (Indeg) Index, Symmetric Division (Deg) Index, Forgotten Indices M-polynomials of Fenofibrate are com

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24

Türkmen, Burcu Nişancı, and Gülçin Karaca. "Finitely Generated Simple Graphs." International Journal of Applied Sciences and Smart Technologies 5, no. 2 (2023): 191–200. http://dx.doi.org/10.24071/ijasst.v5i2.6739.

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In this paper, Kirchhoff, Hyper-Wiener, Randic, Szeged, Pi index calculations of finitely generated (cyclic) simple graphs on the samples were made and classification of some finitely generated (cyclic) groups was achieved with the help of graph theory.

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Fazal Dayan, Muhammad Javaid, and Muhammad Aziz ur Rehman. "On Leap Reduced Reciprocal Randic and Leap Reduced Second Zagreb Indices of Some Graphs." Scientific Inquiry and Review 3, no. 2 (2019): 27–35. http://dx.doi.org/10.32350/sir.32.04.

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Naji et al. introduced the leap Zagreb indices of a graph in 2017 which are new distance-degree-based topological indices conceived depending on the second degree of vertices. In this paper, we have defined the first and second leap reduced reciprocal Randic index and leap reduced second Zagreb index for selected wheel related graphs.

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Reddy, P. S. K., K. N. Prakasha, and Ismail Naci Cangul. "Randic Type Hadi Energy of a Graph." Nepali Mathematical Sciences Report 39, no. 2 (2022): 95–105. http://dx.doi.org/10.3126/nmsr.v39i2.51700.

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Randić index is one of the most famous topological graph indices. The energy of a graph was defined more than four decades ago for its molecular applications. The classical energy of a graph modeling a molecule is defined as the sum of absolute values of all the eigenvalues of the adjacency matrix corresponding to the modeling graph. There are several other versions of the energy notion obtained using other types of graph matrices. In this paper, we are introducing and investigating the Randić type Hadi energy RHE(G) of a graph G, determine several properties of it, and calculate RHE(G) for se

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Ghoffari, Lalu Hasan, I. Gede Adhitya Wisnu Wardhana, and Abdurahim Abdurahim. "Indeks Padmakar-Ivan dan indeks Randic pada graf non-koprima dari grup bilangan bulat modulo." Majalah Ilmiah Matematika dan Statistika 24, no. 1 (2024): 73. http://dx.doi.org/10.19184/mims.v24i1.45367.

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Graph theory, introduced by the Swiss mathematician Leonhard Euler in 1736, has played a pivotal role in solving real-world problems since its inception, notably exemplified by Euler's solution to the Konigsberg Bridge problem. Its applications extend to various domains, including scheduling, shortest path routing, and chemical structure representation. In chemistry, graphs are extensively used to depict molecular structures and chemical compounds, aiding in visualizing atomic connections and overall compound configurations. Topology indices, such as the Padmakar-Ivan (PI) and Randic indices,

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28

Kupchik, Eugene J. "General Treatment of Heteroatoms with the Randic Molecular Connectivity Index." Quantitative Structure-Activity Relationships 8, no. 2 (1989): 98–103. http://dx.doi.org/10.1002/qsar.19890080204.

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29

Javaid, Muhammad, Muhammad Ibraheem, and Ebenezer Bonyah. "Computing Bounds for General Randic Coindex of Sum Graphs." Journal of Mathematics 2021 (December 26, 2021): 1–17. http://dx.doi.org/10.1155/2021/3404236.

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The physical and structural properties of molecular structure or graph such as boiling point, melting point, surface tension, or solubility are studied using topological index (TI). Topological index is a mathematical formula that can be applied to any graph which models some molecular structures. The various operations play an important role in graph theory such as joining, union, intersection, products, and subdivision. In this paper, we computed the bounds for general Randic coindex of F -sum graphs such as ( S -sum, R -sum, Q -sum, and T -sum) in the form of their factor graphs. At the end

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Idrees, Nazeran, Muhammad Jawwad Saif, Afshan Sadiq, Asia Rauf, and Fida Hussain. "Topological Indices of H-Naphtalenic Nanosheet." Open Chemistry 16, no. 1 (2018): 1184–88. http://dx.doi.org/10.1515/chem-2018-0131.

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AbstractIn chemical graph theory, a single numeric number related to a chemical structure is called a topological descriptor or topological index of a graph. In this paper, we compute analytically certain topological indices for H-Naphtalenic nanosheet like Randic index, first Zagreb index, second Zagreb index, geometric arithmetic index, atom bond connectivity index, sum connectivity index and hyper-Zagreb index using edge partition technique. The first multiple Zagreb index and the second multiple Zagreb index of the nanosheet are also discussed in this paper.

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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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32

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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33

Bhatti, Faqir M., Muhammad Malooq, Jihad Ahmad, Iqra Zaman, and Muhammad Usman. "On Some Structural Properties of Integer-Based Graphs and Their Topological Indices." Journal of Mathematics 2022 (August 21, 2022): 1–6. http://dx.doi.org/10.1155/2022/5481940.

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Integer partition plays an important role in different fields like graph theory and number theory. This paper comprises different properties of the integer partition-based graphs. These properties give an idea about the structural properties like degree of the vertices. Furthermore, topological index of the graphs is considered as a transformation of a chemical structure into an integer number. We discussed two very important indices, namely, harmonic index and Randic index, for these particular graphs.

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Xu, Kexiang, Hongshuang Liu, Yujun Yang, and Kinkar Das. "The minimal Kirchhoff index of graphs with a given number of cut vertices." Filomat 30, no. 13 (2016): 3451–63. http://dx.doi.org/10.2298/fil1613451x.

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The resistance distance was introduced by Klein and Randic as a generalization of the classical distance. The Kirchhoff index Kf (G) of a graph G is the sum of resistance distances between all unordered pairs of vertices. In this paper we determine the extremal graphs with minimal Kirchhoff index among all n-vertex graphs with k cut vertices where 1 ? k < n/2.

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MILOVANOVIC, I. Z., P. M. BEKAKOS, M. P. BEKAKOS, and E. I. MILOVANOVIC. "Remark on upper bounds of Randi´c index of a graph." Creative Mathematics and Informatics 25, no. 1 (2016): 71–75. http://dx.doi.org/10.37193/cmi.2016.01.09.

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Let G = (V, E) be an undirected simple graph of order n with m edges without isolated vertices. Further, let d1 ≥ d2 ≥ · · · ≥ dn be vertex degree sequence of G. General Randic index of graph ´ G = (V, E) is defined by Rα = X (i,j)∈E (didj ) α, where α ∈ R − {0}. We consider the case when α = −1 and obtain upper bound for R−1.

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36

P., Gayathri, and Priyanka U. "DEGREE BASED TOPOLOGICAL INDICES OF BANANA TREE GRAPH." International Journal of Current Research and Modern Education, Special Issue (August 13, 2017): 13–24. https://doi.org/10.5281/zenodo.842196.

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Banana tree, is defined by a graph obtained by connecting one leaf of each of p copies of q-star graphs with a single root vertex that is distinct from all the stars, .The degree based indices like Randic Index, Geometric-Arithmetic Index, Sum-Connectivity Index, Harmonic Index, First Zagreb, Second Zagreb, Second Modified Zagreb, Inverse sum, Albertson, Atom Bond connectivity, Symmetric Division Index and Augmented Zagreb index of B(p,q) are computed and derived as a closed formula in two variables p and q and the results are tabulated as a ready reckoner.

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37

Roslly, Siti Rosllydia Dania, Nur Fatimah Az Zahra Ab Halem, Nur Syasya Sahira Zailani, Nur Idayu Alimon, and Siti Afiqah Mohammad. "Generalization of Randic ́ Index of the Non-commuting Graph for Some Finite Groups." Malaysian Journal of Fundamental and Applied Sciences 19, no. 5 (2023): 762–68. http://dx.doi.org/10.11113/mjfas.v19n5.3047.

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Randić index is one of the classical graph-based molecular structure descriptors in the field of mathematical chemistry. The Randić index of a graph is calculated by summing the reciprocals of the square root of the product of the degrees of two adjacent vertices in the graph. Meanwhile, the non-commuting graph is the graph of vertex set whose vertices are non-central elements and two distinct vertices are joined by an edge if and only if they do not commute. In this paper, the general formula of the Randić index of the non-commuting graph associated to three types of finite groups are present

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38

You, Zhifu, and Bolian Liu. "On a conjecture between Randic index and average distance of unicyclic graphs." Filomat 28, no. 4 (2014): 767–73. http://dx.doi.org/10.2298/fil1404767y.

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The Randic index R(G) of a graph G is defined as R(G) = ?uv?E (d(u)d(v))-1/2 where the summation goes over all edges of G. In 1988, Fajtlowicz proposed a conjecture: For all connected graphs G with average distance ad(G), then R(G) ? ad(G). In this paper, we prove that this conjecture is true for unicyclic graphs.

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39

Nasir, Sumiya, Fozia Bashir Farooq, Nazeran Idrees, Muhammad Jawwad Saif, and Fatima Saeed. "Topological Characterization of Nanosheet Covered by C3 and C6." Processes 7, no. 7 (2019): 462. http://dx.doi.org/10.3390/pr7070462.

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A topological index of a graph is a single numeric quantity which relates the chemical structure with its underlying physical and chemical properties. Topological indices of a nanosheet can help us to understand the properties of the material better. This study deals with computation of degree-dependent topological indices like the Randic index, first Zagreb index, second Zagreb index, geometric arithmetic index, atom bond connectivity index, sum connectivity index and hyper Zagreb index of nanosheet covered by C3 and C6. Furthermore, M-polynomial of the nanosheet is also computed, which provi

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Afzal, Deeba, Saira Hameed, Usman Ashraf, Arif Mehmood, Faryal Chaudhry, and Dhan Kumari Thapa. "Study of Neighborhood Degree-Based Topological Indices via Direct and NM-Polynomial of Starphene Graph." Journal of Function Spaces 2022 (June 15, 2022): 1–16. http://dx.doi.org/10.1155/2022/8661489.

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Our objective is to compute the neighborhood degree-based topological indices via NM-polynomial for starphene. In the neighborhood degree-based topological indices, we compute the third version of the Zagreb index; neighborhood second Zagreb index; neighborhood forgotten topological index; neighborhood second modified Zagreb index; neighborhood general Randic index; neighborhood harmonic index; neighborhood inverse sum index; first, second, third, fourth, and fifth NDe indices; fourth atom bond connective index; fifth geometric arithmetic index; fifth arithmetic-geometric index; fifth hyper-fi

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Ahmad, Mukhtar, Muhammad Jafar Hussain, Gulnaz Atta, Sajid Raza, Irfan Waheed, and Ather Qayyum. "Topological Evaluation of Four Para-Line Graphs Absolute Pentacene Graphs Using Topological Indices." International Journal of Analysis and Applications 21 (July 10, 2023): 66. http://dx.doi.org/10.28924/2291-8639-21-2023-66.

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A real-number to molecular structure mapping is a topological index. It is a graph invariant method for describing physico-chemical properties of molecular structures specific substances. In that article, We examined pentacene’s chemical composition. The research on the subsequent indices is reflected in our paper, we conducted an analysis of several indices including general randic connectivity index, first general zagreb index, general sum-connectivity index, atomic bond connectivity index, geometric-arithmetic index, fifth class of geometric-arithmetic indices, hyper-zagreb index, first and

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Zhang, Xiujun, and Muhammad Aamer Rashid. "Sharp Bounds for the General Randic Index of \(R\)-Graph Products." Ars Combinatoria 159, no. 1 (2024): 41–50. http://dx.doi.org/10.61091/ars159-05.

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A chemical structure specifies the molecular geometry of a given molecule or solid in the form of atom arrangements. One way to analyze its properties is to simulate its formation as a product of two or more simpler graphs. In this article, we take this idea to find upper and lower bounds for the generalized Randić index \(\mathcal{R}_{\alpha}\) of four types of graph products, using combinatorial inequalities. We finish this paper by providing the bounds for \(\mathcal{R}_{\alpha}\) of a line graph and rooted product of graphs.

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Imran, Shahid, Muhammad Mudassar Raza, Niat Nigar, Syed Ajaz K. Kirmani, and Fikre Bogale Petros. "Computing Topological Indices and Polynomials of the Rhenium Trioxide." Journal of Mathematics 2022 (August 10, 2022): 1–12. http://dx.doi.org/10.1155/2022/4838327.

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In the study of mathematical chemistry and chemical graph theory, a topological index, also known as a connectivity index, is the arithmetical framework of a graph that specifies its topology and also graph invariant. These topological indices are used to model quantitative structure relationships Q S A R s , which are connections between the work of biological or other molecular structures and the chemical structures. This study computed the first, second, and Hyper Zagreb indices, as well as Zagreb polynomials, Redefined Zagreb indices, Randic index, A B C index, and G A index of chemical st

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Maria, Sambo, Muhammad Shafii Abubakar, Joseph Malose Fatlane, and Kazeem Olalekan Aremu. "Modeling the Physical Properties of Cholera Treatment Drugs via Neighborhood Sum Degree-Based Topological Indices." International Journal of Analysis and Applications 23 (July 16, 2025): 171. https://doi.org/10.28924/2291-8639-23-2025-171.

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Cholera remains a global health challenge, which requires the optimization of treatment strategies, including the design of effective drugs. This study explores the utility of neighborhood sum degree-based topological indices (TIs) in predicting the physical properties of cholera treatment drugs through quantitative structure-property relationship (QSPR) modeling. Eight TIs, neighborhood first Zagreb, second Zagreb, hyper Zagreb, geometric-arithmetic, forgotten, harmonic, Randi´c and atom bond connectivity indices were evaluated using linear regression models across six physicochemical propert

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Mahboob, Abid, Dalal Alrowaili, Sajid Mahboob Alam, Rifaqat Ali, Muhammad Waheed Rasheed, and Imran Siddique. "Topological Attributes of Silicon Carbide Si C 4 - II i , j Based on Ve-Degree and Ev-Degree." Journal of Chemistry 2022 (April 7, 2022): 1–11. http://dx.doi.org/10.1155/2022/3188993.

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The study of graphs containing edges and nodes is of great importance in science and in real life. Topological indices TIs are numerical parameters linked to chemical graphs used to estimate the biological, toxicological, and physical properties of chemical compounds. Recently, two terms, ev-degree- and ve-degree-based TIs, have been defined in chemical graph theory. In this paper, we have estimated degree-based TIs, namely, ev-degree Zagreb M type index, ev-degree Randic R index, ve-degree atom-bond connectivity ABC index, ve-degree geometric arithmetic index GA , ve-degree harmonic H index,

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Mufti, Zeeshan Saleem, Rukhshanda Anjum, Ferdous M. O. Tawfiq, Ali Tabraiz, Qin Xin, and Dilruba Akter. "Fuzzy Topological Characterization of q C n Graph via Fuzzy Topological Indices." Journal of Mathematics 2023 (September 11, 2023): 1–11. http://dx.doi.org/10.1155/2023/5141179.

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Fuzzy topological indices are one of the accomplished mathematical approaches for numerous technology, engineering, and real-world problems such as telecommunications, social networking, traffic light controls, marine, neural networks, Internet routing, and wireless sensor network (Muneera et al. (2021)). This manuscript comprises the study of a particular class of graphs known as q C n snake graphs. Some innovative results regarding fuzzy topological indices have been established. The major goal of the work is to introduce the notions of First Fuzzy Zagrab Index, Second Fuzzy Zagrab Index, Ra

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Saeed, Nouman, Kai Long, Zeeshan Saleem Mufti, Hafsa Sajid, and Abdul Rehman. "Degree-Based Topological Indices of Boron B12." Journal of Chemistry 2021 (March 29, 2021): 1–6. http://dx.doi.org/10.1155/2021/5563218.

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Topological index sometimes called molecular descriptor is a numerical value which associates a chemical composition for correlating chemical structure with numerous physical properties, chemical reactivity, or biological activity. In this paper, we study some topological indices of boron and try to correlate the physicochemical properties such as freezing points, boiling points, melting points, infrared spectrum, electronic parameters, viscosity, and density of chemical graphs. We discuss these topological indices, and some of them are mentioned here such as Randic index, the first general Za

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Afzal, Farkhanda, Mohammad Zeeshan, Deeba Afzal, Sufian Munawar, Dhan Kumari Thapa, and Alina Mirza. "New Degree-Based Topological Indices of Toroidal Polyhex Graph by Means of M-Polynomial." Journal of Mathematics 2022 (May 11, 2022): 1–5. http://dx.doi.org/10.1155/2022/1228203.

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Graph theory is the principal field of mathematics. In this manuscript, we have discussed the toroidal polyhex graph. Some new indices such as reduced reciprocal randic, arithmetic geometric, SK, SK1, SK2 indices, First Zagrab, the general sum-connectivity, SCIλ, and the forgotten index have been used. We have computed the closed form of topological indices of toroidal polyhex graph via M-Polynomial.

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Liu, Jianxi. "On the variation of the Randic index with given girth and leaves." Filomat 28, no. 9 (2014): 1849–53. http://dx.doi.org/10.2298/fil1409849l.

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The variation of Randic index R'(G) of a graph G is defined by R'(G) = ?uv 1/ max{du,dv}, where du is the degree of a vertex u in G and the summation extends over all edges uv of G. In this work, we characterize the extremal trees achieving the minimum value of R0 for trees with given number of vertices and leaves. Furthermore, we characterize the extremal graphs achieving the minimum value of R' for connected graphs with given number of vertices and girth.

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Aftab, Muhammad Haroon, Muhammad Rafaqat, M. Hussain, and Tariq Zia. "On the Computation of Some Topological Descriptors to Find Closed Formulas for Certain Chemical Graphs." Journal of Chemistry 2021 (May 21, 2021): 1–16. http://dx.doi.org/10.1155/2021/5533619.

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In this research paper, we will compute the topological indices (degree based) such as the ordinary generalized geometric-arithmetic (OGA) index, first and second Gourava indices, first and second hyper-Gourava indices, general Randic´ index R γ G , for γ = ± 1 , ± 1 / 2 , harmonic index, general version of the harmonic index, atom-bond connectivity (ABC) index, SK, SK1, and SK2 indices, sum-connectivity index, general sum-connectivity index, and first general Zagreb and forgotten topological indices for various types of chemical networks such as the subdivided polythiophene network, subdivide

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