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Journal articles on the topic 'Reciprocal molecular topological index'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Zhou, Bo, and Nenad Trinajstić. "On reciprocal molecular topological index." Journal of Mathematical Chemistry 44, no. 1 (2007): 235–43. http://dx.doi.org/10.1007/s10910-007-9306-y.

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2

Albalahi, Abeer M., Zhibin Du, Akbar Ali, Muhammad Javaid, and Amjad E. Hamza. "On the Sum of a Topological Index and Its Reciprocal Index for Unicyclic Graphs." Match Communications in Mathematical and in Computer Chemistry 93, no. 3 (2024): 839–52. https://doi.org/10.46793/match.93-3.839a.

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This paper gives the optimal values of the sum of a topological index and its reciprocal version of fixed-order unicyclic graphs for the cases of the first Zagreb index, second Zagreb index, forgotten topological index, and Sombor index. For each of the aforementioned four topological indices, the cycle graph uniquely attains the minimum value of the mentioned sum and the graph formed by inserting one edge in the star graph uniquely attains the maximum value of this sum in the considered class of graphs. These findings extend the results of the recent paper [W. Gao, MATCH Commun. Math. Comput.

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3

Ali, Fawad, Bilal A. Rather, Nahid Fatima, et al. "On the Topological Indices of Commuting Graphs for Finite Non-Abelian Groups." Symmetry 14, no. 6 (2022): 1266. http://dx.doi.org/10.3390/sym14061266.

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A topological index is a number generated from a molecular structure (i.e., a graph) that indicates the essential structural properties of the proposed molecule. Indeed, it is an algebraic quantity connected with the chemical structure that correlates it with various physical characteristics. It is possible to determine several different properties, such as chemical activity, thermodynamic properties, physicochemical activity, and biological activity, using several topological indices, such as the geometric-arithmetic index, arithmetic-geometric index, Randić index, and the atom-bond connectiv

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4

Wei, Chang-Cheng, Muhammad Salman, Usman Ali, et al. "Some Topological Invariants of Graphs Associated with the Group of Symmetries." Journal of Chemistry 2020 (March 9, 2020): 1–13. http://dx.doi.org/10.1155/2020/6289518.

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A topological index is a quantity that is somehow calculated from a graph (molecular structure), which reflects relevant structural features of the underlying molecule. It is, in fact, a numerical value associated with the chemical constitution for the correlation of chemical structures with various physical properties, chemical reactivity, or biological activity. A large number of properties like physicochemical properties, thermodynamic properties, chemical activity, and biological activity can be determined with the help of various topological indices such as atom-bond connectivity indices,

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5

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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6

Ali, Fawad, Bilal Ahmad Rather, Muhammad Sarfraz, Asad Ullah, Nahid Fatima, and Wali Khan Mashwani. "Certain Topological Indices of Non-Commuting Graphs for Finite Non-Abelian Groups." Molecules 27, no. 18 (2022): 6053. http://dx.doi.org/10.3390/molecules27186053.

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A topological index is a number derived from a molecular structure (i.e., a graph) that represents the fundamental structural characteristics of a suggested molecule. Various topological indices, including the atom-bond connectivity index, the geometric–arithmetic index, and the Randić index, can be utilized to determine various characteristics, such as physicochemical activity, chemical activity, and thermodynamic properties. Meanwhile, the non-commuting graph ΓG of a finite group G is a graph where non-central elements of G are its vertex set, while two different elements are edge connected

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7

Saleh, Anwar, and Samirah H. Alsulami. "On the Entire Harmonic Index and Entire Harmonic Polynomial of Graphs." Symmetry 16, no. 2 (2024): 208. http://dx.doi.org/10.3390/sym16020208.

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A topological descriptor is a numerical parameter that describes a chemical structure using the related molecular graph. Topological descriptors have significance in mathematical chemistry, particularly for studying QSPR and QSAR. In addition, if a topological descriptor has a reciprocal link with a molecular attribute, it is referred to as a topological index. The use of topological indices can help to examine the physicochemical features of chemical compounds because they encode certain attributes of a molecule. The Randić index is a molecular structure descriptor that has several applicatio

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8

Kulli, V. R. "Computation of Minus F-indices and their Polynomials of Titania Nanotubes." Annals of Pure and Applied Mathematics 22, no. 02 (2020): 137–42. http://dx.doi.org/10.22457/apam.v22n2a09802.

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In Chemical Graph Theory, a forgotten topological index or F-index has significant importance to collect information about properties of chemical compounds. In this study, we introduce the modified minus F-index, minus connectivity F-index, reciprocal minus connectivity F-index, general minus F-index and their polynomials of a molecular graph. Furthermore, we present exact expressions for these minus F-indices and their polynomials of titania nanotubes.

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9

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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10

Guirao, Juan L. G., Muhammad Imran, Muhammad Kamran Siddiqui, and Shehnaz Akhter. "On Valency-Based Molecular Topological Descriptors of Subdivision Vertex-Edge Join of Three Graphs." Symmetry 12, no. 6 (2020): 1026. http://dx.doi.org/10.3390/sym12061026.

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In the studies of quantitative structure–activity relationships (QSARs) and quantitative structure–property relationships (QSPRs), graph invariants are used to estimate the biological activities and properties of chemical compounds. In these studies, degree-based topological indices have a significant place among the other descriptors because of the ease of generation and the speed with which these computations can be accomplished. In this paper, we give the results related to the first, second, and third Zagreb indices, forgotten index, hyper Zagreb index, reduced first and second Zagreb indi

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11

Abbas, Ghulam, Anam Rani, Muhammad Salman, Tahira Noreen, and Usman Ali. "Hosoya properties of the commuting graph associated with the group of symmetries." Main Group Metal Chemistry 44, no. 1 (2021): 173–84. http://dx.doi.org/10.1515/mgmc-2021-0017.

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Abstract A vast amount of information about distance based graph invariants is contained in the Hosoya polynomial. Such an information is helpful to determine well-known distance based molecular descriptors. The Hosoya index or Z-index of a graph G is the total number of its matching. The Hosoya index is a prominent example of topological indices, which are of great interest in combinatorial chemistry, and later on it applies to address several chemical properties in molecular structures. In this article, we investigate Hosoya properties (Hosoya polynomial, reciprocal Hosoya polynomial and Hos

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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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13

Yao, Gang, Khian-Hooi Chew, Yan Wu, Yuhua Li, and Rui-Pin Chen. "Propagation dynamics of vector vortex beams in a strongly nonlocal nonlinear medium with parity-time-symmetric potentials." Journal of Optics 24, no. 3 (2022): 035606. http://dx.doi.org/10.1088/2040-8986/ac4e5f.

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Abstract We demonstrate the dynamical properties of a vector vortex optical field (VVOF) in a strongly nonlocal nonlinear medium (SNNM) with sine and cosine parity-time-symmetric potentials (SCPT) by using the coupled vector Snyder-Mitchell model. Our study shows that the shape of the optical field is chaotically distorted in different propagation distances due to the modulation of complex refractive index. Despite the distorted optical field, the VVOF reciprocally evolves in a periodic stretch and shrink behavior during propagation in the SNNM-SCPT. The reciprocal conversions between the line

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14

Ali, Fawad, Bilal Ahmad Rather, Anwarud Din, Tareq Saeed, and Asad Ullah. "Power Graphs of Finite Groups Determined by Hosoya Properties." Entropy 24, no. 2 (2022): 213. http://dx.doi.org/10.3390/e24020213.

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Suppose G is a finite group. The power graph represented by P(G) of G is a graph, whose node set is G, and two different elements are adjacent if and only if one is an integral power of the other. The Hosoya polynomial contains much information regarding graph invariants depending on the distance. In this article, we discuss the Hosoya characteristics (the Hosoya polynomial and its reciprocal) of the power graph related to an algebraic structure formed by the symmetries of regular molecular gones. As a consequence, we determined the Hosoya index of the power graphs of the dihedral and the gene

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15

Rather, Bilal Ahmad, Fawad Ali, Suliman Alsaeed, and Muhammad Naeem. "Hosoya Polynomials of Power Graphs of Certain Finite Groups." Molecules 27, no. 18 (2022): 6081. http://dx.doi.org/10.3390/molecules27186081.

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Assume that G is a finite group. The power graph P(G) of G is a graph in which G is its node set, where two different elements are connected by an edge whenever one of them is a power of the other. A topological index is a number generated from a molecular structure that indicates important structural properties of the proposed molecule. Indeed, it is a numerical quantity connected with the chemical composition that is used to correlate chemical structures with various physical characteristics, chemical reactivity, and biological activity. This information is important for identifying well-kno

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16

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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17

Kanwal, Salma, Shanshan Shang, Muhammad Kamran Siddiqui, Tahira Sumbal Shaikh, Ammara Afzal, and Anton Asare-Tuah. "On Analysis of Topological Aspects for Subdivision of Kragujevac Tree Networks." Mathematical Problems in Engineering 2021 (November 3, 2021): 1–15. http://dx.doi.org/10.1155/2021/9082320.

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In this paper, we have taken review of certain topological topological characteristics of subdivision and the line graph of subdivision of Kragujevac tree. A Kragujevac tree is denoted by K , K ∈ Kg q = r 2 t + 1 + 1 , r , with order r 2 t + 1 + 1 and size r 2 t + 1 , respectively. We have computed the Zagreb polynomials, forgotten polynomial, and M-polynomial for Kragujevac tree. Moreover, we have computed topological indices like Zagreb-type indices, reduced reciprocal Randić indices, family of Gourava indices as well as forgotten index. Further, some topological indices that can be directly

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18

Gao, Wei. "The Sum of a Topological Index and Its Reciprocal Index." Match Communications in Mathematical and in Computer Chemistry 93, no. 2 (2024): 535–47. http://dx.doi.org/10.46793/match.93-2.535g.

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19

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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20

Mueller, Wolfgang R., Klaus Szymanski, Jan V. Knop, and Nenad Trinajstic. "Molecular topological index." Journal of Chemical Information and Modeling 30, no. 2 (1990): 160–63. http://dx.doi.org/10.1021/ci00066a011.

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21

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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22

Raji, M., and G. Jayalalitha. "Harary Index of Anthracene’s Chemical Graph Using Domination." Webology 18, Special Issue 01 (2021): 107–11. http://dx.doi.org/10.14704/web/v18si01/web18047.

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Consider a Anthracene’s Chemical Graph as a connected finite simple graph. In such a chemical graph, vertices and edges signify atoms and bonds respectively. Harary Index is a distance based on the topological index. This paper obtains Harary Index of Chemical Graph of Anthracene using Reciprocal Minimum Dominating Distance Matrix.

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23

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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24

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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25

Rechtsman, Mikael C. "Reciprocal topological photonic crystals allow backscattering." Nature Photonics 17, no. 5 (2023): 383–84. http://dx.doi.org/10.1038/s41566-023-01199-9.

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26

Shanmukha, M. C., K. N. Anil Kumar, N. S. Basavarajappa, and A. Usha. "NEIGHBORHOOD TOPOLOGICAL INDICES OF METAL-ORGANIC NETWORKS." Jnanabha 52, no. 01 (2022): 174–81. http://dx.doi.org/10.58250/jnanabha.2022.52123.

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A group of chemical compounds containing organic ligands and metal ions(clusters) called as Metal organic networks (MON s). These are found as one, two and three dimensional structures of porous and subordinate class of coordination polymers. The characteristics of MON s are high surface area, large pore volume, different morphology and very good chemical stability. The applications of MON s includes gas storage, heterogeneous catalysis and sensing of various gases. The stability and characteristics of these networks have become important because of the above said characteristics. The numerica

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27

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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Ramane, Harishchandra S., Deepa V. Kitturmath, and Kavita Bhajantri. "Transmission-reciprocal transmission index and coindex of graphs." Acta Universitatis Sapientiae, Informatica 14, no. 1 (2022): 84–103. http://dx.doi.org/10.2478/ausi-2022-0006.

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Abstract The transmission of a vertex u in a connected graph G is defined as σ(u) = Σv∈V(G) d(u, v) and reciprocal transmission of a vertex u is defined as r s ( u ) = ∑ v ∈ V ( G ) 1 d ( u , v ) rs(u) = \sum\nolimits_{v \in V\left( G \right)} {{1 \over {d\left( {u,v} \right)}}} , where d(u, v) is the distance between vertex u and v in G. In this paper we define new distance based topological index of a connected graph G called transmission-reciprocal transmission index T R T ( G ) = ∑ u v ∈ E ( G ) ( σ ( u ) r s ( u ) + σ ( v ) r s ( v ) ) TRT\left( G \right) = \sum\nolimits_{uv \in E\left( G

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29

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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30

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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31

Magi, P. M. "ON THE TOPOLOGICAL INDICES OF WEAKLY ZERO-DIVISOR GRAPH." Advances in Mathematics: Scientific Journal 14, no. 2 (2025): 201–10. https://doi.org/10.37418/amsj.14.2.5.

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The Wiener index of a connected graph $G$ is defined as $W(G)=\linebreak \sum_{u, v} d_{G}(u, v)$, where $d_{G}(u, v)$ denotes the distance between the vertices $u$ and $v$ and the sum runs over all unordered pairs of vertices. The Harary index of a connected graph $G$ is the sum of reciprocal of distances between all pairs of vertices i.e. $H(G)= \sum \frac{1}{d_G(u,v) }$, where the summation runs over all unordered pairs u and v of vertices of $G$. The weakly zero-divisor graph of a commutative ring $R$ ( $\Gamma' (R)$) is a simple undirected graph with vertex set as the set of all non zero

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32

An, Mingqiang. "On Hamiltonian properties of bipartite graphs and several topological indices." Filomat 38, no. 20 (2024): 7209–14. https://doi.org/10.2298/fil2420209a.

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For a connected graph H, the first Zagreb index M1(H) is equal to the sum of squares of the degrees of the vertices of H. The reciprocal degree distance of H, denoted by RDD(H), is defined as RDD(H) = ?x?y degH(x) + degH(y)/distH(x,y), where degH(x) is the degree of the vertex x in H and distH(x, y) denotes the distance between two vertices x and y in H. The forgotten topological index F(H) of H is the sum of cubes of all its vertex degrees. In this paper, we give a best possible lower bound on M1(H), RDD(H) or F(H) to ensure that a bipartite graph H is Hamiltonian.

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33

Hu, Chang-Yu, and Lu Xu. "On Highly Discriminating Molecular Topological Index." Journal of Chemical Information and Computer Sciences 36, no. 1 (1996): 82–90. http://dx.doi.org/10.1021/ci9501150.

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34

J. Gowria and J. Jayapriya. "Labeling on Molecular Graph inducing Topological Indices." Bioscan 20, no. 1 (2025): 664–70. https://doi.org/10.63001/tbs.2025.v20.i01.pp664-670.

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Graph labeling is the assignment of integers to vertices or edges or both under certain conditions. In this article, we link graph label-ing and topological indices as concepts. We introduce topological indices in particular for specific molecular graphs that permit HMC labeling. The concept of graphs is playing a significant role in the examination of QSPR data using topological indices. This part considers the labeled square index SQI(G), labeled product index PI(G), labeled sum index SI(G), labeled Nirmala index NI(G), labeled Sombor index SOLI(G), labeled forgotten index FI(G), and the gro

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35

Klein, Douglas J., Zlatko Mihalic, Dejan Plavsic, and Nenad Trinajstic. "Molecular topological index: a relation with the Wiener index." Journal of Chemical Information and Modeling 32, no. 4 (1992): 304–5. http://dx.doi.org/10.1021/ci00008a008.

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36

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

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The degree-based topological indices correlate certain physicochemical properties such as boiling point, strain energy, and stability, etc., of certain chemical compounds. Among the major classes of topological indices are the distance-based topological indices, degree-based topological indices, and counting-related polynomials and corresponding indices of graphs. Among all of the degree-based indices, namely the first general Zagreb index, general Rndić connectivity index, general sum-connectivity index, atom–bond connectivity index (ABC), and geometric–arithmetic index (GA), are most importa

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37

Cao, Yafei, Yuanwei Yao, and Huiping Feng. "Schoch Effect in Topological Phononic Crystals." Academic Journal of Science and Technology 5, no. 2 (2023): 89–94. http://dx.doi.org/10.54097/ajst.v5i2.6289.

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This article investigates the Schoch negative displacement phenomenon at the interface between two-dimensional topological acoustic materials and traditional materials. The results show that a negative Schoch displacement occurs at the frequency of the Dirac point in the phononic crystal. At this point, the reciprocal of the effective bulk modulus of the phononic crystal tends to zero, making it an acoustic metamaterial with a refractive index close to zero. At the same time, the maximum value of the effective impedance of the phononic crystal and the real part of the reflection coefficient un

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Mohanappriya, G., and D. Vijiyalakshmi. "Edge Version Molecular Descriptors of Tetrameric 1, 3 Adamantane." International Journal of Engineering & Technology 7, no. 4.10 (2018): 403. http://dx.doi.org/10.14419/ijet.v7i4.10.21026.

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Molecular descriptors (Topological indices) are the numerical invariants of a molecular graph which distinguish its topology. In this article, we compute edge version of topological indices such as Zagreb index, Atom bond connectivity index, Fourth atom bond connectivity index, Geometric Arithmetic index and Fifth Geometric Arithmetic index of tetrameric 1,3 adamantane.

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Nikolić, Sonja, Nenad Trinajstić, and Zlatko Mihalid. "Molecular topological index: An extension to heterosystems." Journal of Mathematical Chemistry 12, no. 1 (1993): 251–64. http://dx.doi.org/10.1007/bf01164639.

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SHAO, ZEHUI, HUIQIN JIANG, and ZAHID RAZA. "Inequalities Among Topological Descriptors." Kragujevac Journal of Mathematics 47, no. 5 (2023): 661–72. http://dx.doi.org/10.46793/kgjmat2305.661s.

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A topological index is a type of molecular descriptor that is calculated based on the molecular graph of a chemical compound. Topological indices are used for example in the development of QSAR QSPR in which the biological activity or other properties of molecules are correlated with their chemical structure. In this paper, we establish several inequalities among the molecular descriptors such as the generalized version of the ﬁrst Zagreb index, the Randić index, the ABC index, AZI index, and the redeﬁned ﬁrst, second and third Zagreb indices.

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Schultz, Harry P., and Tor P. Schultz. "Topological Organic Chemistry. 11. Graph Theory and Reciprocal Schultz-Type Molecular Topological Indices of Alkanes and Cycloalkanes." Journal of Chemical Information and Computer Sciences 38, no. 5 (1998): 853–57. http://dx.doi.org/10.1021/ci9800312.

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Yang, Hong, Muhammad Aamer Rashid, Sarfraz Ahmad, Saima Sami Khan, and Muhammad Kamran Siddiqui. "On Molecular Descriptors of Face-Centered Cubic Lattice." Processes 7, no. 5 (2019): 280. http://dx.doi.org/10.3390/pr7050280.

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Face-centered cubic lattice F C C ( n ) has received extensive consideration as of late, inferable from its recognized properties and non-poisonous nature, minimal effort, plenitude, and basic creation process. The graph of a face-centered cubic cross-section contains cube points and face centres. A topological index of a molecular graph G is a numeric amount identified with G, which depicts its topological properties. In this paper, using graph theory tools, we computed the molecular descriptors (topological indices)—to be specific, Zagreb-type indices, a forgotten index, a Balaban index, the

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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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Barman, Jayjit, and Shibsankar Das. "Geometric Approach to Degree-Based Topological Index: Hyperbolic Sombor Index." Match Communications in Mathematical and in Computer Chemistry 95, no. 1 (2025): 63–94. https://doi.org/10.46793/match95-1.03425.

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This article presents a new geometric approach to forming molecular structure descriptors (topological indices) based on vertex degrees. The degrees of a pair of adjacent vertices are represented by the length of the semi-major and semi-minor axes of the hyperbola that form the basis of the model. In this way, a number of previously known topological indices can now be interpreted geometrically and some new topological indices can be generated. The eccentricity of the hyperbola gives rise to a remarkably simple vertex-degree-based topological index, which we refer to as the hyperbolic Sombor i

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S Shenbaga Devi. "Computing topological indices of Porous Graphene." Advances in Nonlinear Variational Inequalities 28, no. 6s (2025): 827–35. https://doi.org/10.52783/anvi.v28.4429.

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Topological indices in chemical graph theory helps to quantify the molecular structure and to analyse the correlation of the structures using physical, chemical, and biological properties. In this paper, we have discussed several degree-based topological indices like first hyper zagreb, second hyper zagreb, reduced second Zagreb, forgotten, harmonic, sombor, arithmetic geometric, reduced reciprocal randic and SS indices for porous graphene. This will be useful for determining the relationship between the mathematical qualities and the characteristics of a specific chemical compound. This study

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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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Islam, Tanweer Ul, Zeeshan Saleem Mufti, Aqsa Ameen, Muhammad Nauman Aslam, and Ali Tabraiz. "On Certain Aspects of Topological Indices." Journal of Mathematics 2021 (May 3, 2021): 1–20. http://dx.doi.org/10.1155/2021/9913529.

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A topological index, also known as connectivity index, is a molecular structure descriptor calculated from a molecular graph of a chemical compound which characterizes its topology. Various topological indices are categorized based on their degree, distance, and spectrum. In this study, we calculated and analyzed the degree-based topological indices such as first general Zagreb index M r G , geometric arithmetic index GA G , harmonic index H G , general version of harmonic index H r G , sum connectivity index λ G , general sum connectivity index λ r G , forgotten topological index F G , and ma

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Asif, Fatima, Agha Kashif, Sohail Zafar, and Michael Onyango Ojiema. "Mostar Index of Cycle-Related Structures." Journal of Chemistry 2022 (March 7, 2022): 1–11. http://dx.doi.org/10.1155/2022/9411947.

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A topological index is a numerical quantity associated with the molecular structure of a chemical compound. This number remains fixed with respect to the symmetry of a molecular graph. Diverse research studies have shown that the topological indices of symmetrical graphs are interrelated with several physiochemical properties such as boiling point, density, and heat of formation. Peripherality is also an important tool to study topological aspects of molecular graphs. Recently, a bond-additive topological index called the Mostar index that measures the peripherality of a graph is investigated

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Hu, Qian-Nan, Yi-Zeng Liang, and Kai-Tai Yi-Zeng. "The Matrix Expression, Topological Index and Atomic Attribute of Molecular Topological Structure." Journal of Data Science 1, no. 4 (2021): 361–89. http://dx.doi.org/10.6339/jds.2003.01(4).172.

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Gutman, Ivan. "Selected properties of the Schultz molecular topological index." Journal of Chemical Information and Modeling 34, no. 5 (1994): 1087–89. http://dx.doi.org/10.1021/ci00021a009.

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