scholarly journals Reformulated Zagreb Indices of Some Derived Graphs

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 366 ◽  
Author(s):  
Jia-Bao Liu ◽  
Bahadur Ali ◽  
Muhammad Aslam Malik ◽  
Hafiz Muhammad Afzal Siddiqui ◽  
Muhammad Imran
Keyword(s):  
Physical Properties ◽  
Chemical Structure ◽  
Topological Index ◽  
Chemical Reactivity ◽  
Line Graph ◽  
Total Graph ◽  
Zagreb Indices ◽  
Subdivision Graph ◽  
Chemical Constitution ◽  
Vertex Degrees

A topological index is a numeric quantity that is closely related to the chemical constitution to establish the correlation of its chemical structure with chemical reactivity or physical properties. Miličević reformulated the original Zagreb indices in 2004, replacing vertex degrees by edge degrees. In this paper, we established the expressions for the reformulated Zagreb indices of some derived graphs such as a complement, line graph, subdivision graph, edge-semitotal graph, vertex-semitotal graph, total graph, and paraline graph of a graph.

scholarly journals Computing Topological Indices and Polynomials for Line Graphs

Mathematics ◽  
2018 ◽  
Vol 6 (8) ◽  
pp. 137 ◽  
Author(s):  
Shahid Imran ◽  
Muhammad Siddiqui ◽  
Muhammad Imran ◽  
Muhammad Nadeem
Keyword(s):  
Topological Index ◽  
Line Graph ◽  
Topological Indices ◽  
Line Graphs ◽  
Zagreb Index ◽  
Zagreb Indices ◽  
Second Zagreb Index ◽  
Vertex Degrees ◽  
Set Up ◽  
Ladder Graphs

A topological index is a number related to the atomic index that allows quantitative structure–action/property/toxicity connections. All the more vital topological indices correspond to certain physico-concoction properties like breaking point, solidness, strain vitality, and so forth, of synthetic mixes. The idea of the hyper Zagreb index, multiple Zagreb indices and Zagreb polynomials was set up in the substance diagram hypothesis in light of vertex degrees. These indices are valuable in the investigation of calming exercises of certain compound systems. In this paper, we computed the first and second Zagreb index, the hyper Zagreb index, multiple Zagreb indices and Zagreb polynomials of the line graph of wheel and ladder graphs by utilizing the idea of subdivision.

scholarly journals QSPR analysis of some novel neighbourhood degree-based topological descriptors

2021 ◽  
Author(s):  
Sourav Mondal ◽  
Arindam Dey ◽  
Nilanjan De ◽  
Anita Pal
Keyword(s):  
Chemical Structure ◽  
Topological Index ◽  
Chemical Reactivity ◽  
Binding Mode ◽  
Topological Descriptors ◽  
The Novel ◽  
Structure Property ◽  
Mathematical Properties ◽  
Structure Property Relationship ◽  
Chemical Constitution

AbstractTopological index is a numerical value associated with a chemical constitution for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. In this work, some new indices based on neighborhood degree sum of nodes are proposed. To make the computation of the novel indices convenient, an algorithm is designed. Quantitative structure property relationship (QSPR) study is a good statistical method for investigating drug activity or binding mode for different receptors. QSPR analysis of the newly introduced indices is studied here which reveals their predicting power. A comparative study of the novel indices with some well-known and mostly used indices in structure-property modelling and isomer discrimination is performed. Some mathematical properties of these indices are also discussed here.

scholarly journals A Computational Approach on Acetaminophen Drug using Degree-Based Topological Indices and M-Polynomials

2021 ◽  
Vol 12 (6) ◽  
pp. 7249-7266
Keyword(s):  
Biological Activity ◽  
Physicochemical Properties ◽  
Chemical Structure ◽  
Topological Index ◽  
Chemical Reactivity ◽  
Chemical Compounds ◽  
Computational Approach ◽  
Topological Indices ◽  
Numerical Representation ◽  
Essential Drug

Topological index is a numerical representation of a chemical structure. Based on these indices, physicochemical properties, thermodynamic behavior, chemical reactivity, and biological activity of chemical compounds are calculated. Acetaminophen is an essential drug to prevent/treat various types of viral fever, including malaria, flu, dengue, SARS, and even COVID-19. This paper computes the sum and multiplicative version of various topological indices such as General Zagreb, General Randić, General OGA, AG, ISI, SDD, Forgotten indices M-polynomials of Acetaminophen. To the best of our knowledge, for the Acetaminophen drugs, these indices have not been computed previously.

scholarly journals Topological properties of Graphene using some novel neighborhood degree-based topological indices

2019 ◽  
Vol 11 (01) ◽  
pp. 1950006 ◽  
Author(s):  
Sourav Mondal ◽  
Nilanjan De ◽  
Anita Pal
Keyword(s):  
Real Number ◽  
Chemical Structure ◽  
Topological Index ◽  
Line Graph ◽  
Topological Indices ◽  
Index Formula ◽  
Topological Properties ◽  
Zagreb Index ◽  
Physiochemical Properties ◽  
Second Zagreb Index

Topological indices are numeric quantities that transform chemical structure to real number. Topological indices are used in QSAR/QSPR studies to correlate the bioactivity and physiochemical properties of molecule. In this paper, some newly designed neighborhood degree-based topological indices named as neighborhood Zagreb index ([Formula: see text]), neighborhood version of Forgotten topological index ([Formula: see text]), modified neighborhood version of Forgotten topological index ([Formula: see text]), neighborhood version of second Zagreb index ([Formula: see text]) and neighborhood version of hyper Zagreb index ([Formula: see text]) are obtained for Graphene and line graph of Graphene using subdivision idea. In addition, these indices are compared graphically with respect to their response for Graphene and line graph of subdivision of Graphene.

scholarly journals Hyperbolicity on Graph Operators

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 360 ◽  
Author(s):  
J. Méndez-Bermúdez ◽  
Rosalío Reyes ◽  
José Rodríguez ◽  
José Sigarreta
Keyword(s):  
Line Graph ◽  
Discrete Mathematics ◽  
Total Graph ◽  
Subdivision Graph ◽  
Gromov Product

A graph operator is a mapping F : Γ → Γ ′ , where Γ and Γ ′ are families of graphs. The different kinds of graph operators are an important topic in Discrete Mathematics and its applications. The symmetry of this operations allows us to prove inequalities relating the hyperbolicity constants of a graph G and its graph operators: line graph, Λ ( G ) ; subdivision graph, S ( G ) ; total graph, T ( G ) ; and the operators R ( G ) and Q ( G ) . In particular, we get relationships such as δ ( G ) ≤ δ ( R ( G ) ) ≤ δ ( G ) + 1 / 2 , δ ( Λ ( G ) ) ≤ δ ( Q ( G ) ) ≤ δ ( Λ ( G ) ) + 1 / 2 , δ ( S ( G ) ) ≤ 2 δ ( R ( G ) ) ≤ δ ( S ( G ) ) + 1 and δ ( R ( G ) ) − 1 / 2 ≤ δ ( Λ ( G ) ) ≤ 5 δ ( R ( G ) ) + 5 / 2 for every graph which is not a tree. Moreover, we also derive some inequalities for the Gromov product and the Gromov product restricted to vertices.

scholarly journals Molecular Descriptors of Nanotube, Oxide, Silicate, and Triangulene Networks

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Wei Gao ◽  
Muhammad Kamran Siddiqui
Keyword(s):  
Molecular Structure ◽  
Carbon Nanotube ◽  
Interconnection Networks ◽  
Chemical Structure ◽  
Chemical Reactivity ◽  
Hexagonal Lattice ◽  
Zagreb Index ◽  
Chemical Graph Theory ◽  
Vertex Degrees ◽  
Carbon Nanotube Networks

A topological index is a real number associated with chemical constitution purporting for correlation of chemical structure with various physical properties, chemical reactivity, or biological activity. The concept of hyper Zagreb index, first multiple Zagreb index, second multiple Zagreb index, and Zagreb polynomials was established in chemical graph theory based on vertex degrees. It is reported that these indices are useful in the study of anti-inflammatory activities of certain chemical networks. In this paper, we study carbon nanotube networks which are motivated by molecular structure of regular hexagonal lattice and also studied interconnection networks which are motivated by molecular structure of a chemical compound SiO4. We determine hyper Zagreb index, first multiple Zagreb index, second multiple Zagreb index, and Zagreb polynomials for some important class of carbon nanotube networks, dominating oxide network, dominating silicate network, and regular triangulene oxide network.

scholarly journals New Results on the Forgotten Topological Index and Coindex

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Akbar Jahanbani ◽  
Maryam Atapour ◽  
Rana Khoeilar
Keyword(s):  
Electron Energy ◽  
Connected Graph ◽  
Topological Index ◽  
Nonadjacent Vertex ◽  
Zagreb Indices ◽  
Vertex Degrees ◽  
Simple Connected Graph

The ℱ -coindex (forgotten topological coindex) for a simple connected graph G is defined as the sum of the terms ζ G 2 y + ζ G 2 x over all nonadjacent vertex pairs x , y of G , where ζ G y and ζ G x are the degrees of the vertices y and x in G , respectively. The ℱ -index of a graph is defined as the sum of cubes of the vertex degrees of the graph. This was introduced in 1972 in the same paper where the first and second Zagreb indices were introduced to study the structure dependency of total π -electron energy. Therefore, considering the importance of the ℱ -index and ℱ -coindex, in this paper, we study these indices, and we present new bounds for the ℱ -index and ℱ -coindex.

scholarly journals On topological properties of block shift and hierarchical hypercube networks

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 810-819
Author(s):  
Juan Luis García Guirao ◽  
Muhammad Kamran Siddiqui ◽  
Asif Hussain
Keyword(s):  
Graph Theory ◽  
Interconnection Networks ◽  
Communication Theory ◽  
Chemical Reactivity ◽  
Zagreb Index ◽  
Electronic Engineering ◽  
Chemical Graph Theory ◽  
Chemical Constitution ◽  
Vertex Degrees ◽  
Hypercube Networks

Abstract Networks play an important role in electrical and electronic engineering. It depends on what area of electrical and electronic engineering, for example there is a lot more abstract mathematics in communication theory and signal processing and networking etc. Networks involve nodes communicating with each other. Graph theory has found a considerable use in this area of research. A topological index is a real number associated with chemical constitution purporting for correlation of chemical networks with various physical properties, chemical reactivity. The concept of hyper Zagreb index, first multiple Zagreb index, second multiple Zagreb index and Zagreb polynomials was established in chemical graph theory based on vertex degrees. In this paper, we extend this study to interconnection networks and derive analytical closed results of hyper Zagreb index, first multiple Zagreb index, second multiple Zagreb index, Zagreb polynomials and redefined Zagreb indices for block shift network (BSN − 1) and (BSN − 2), hierarchical hypercube (HHC − 1) and (HHC − 2).

scholarly journals Topological study of the para-line graphs of certain pentacene via topological indices

2018 ◽  
Vol 16 (1) ◽  
pp. 1200-1206 ◽  
Author(s):  
Zeeshan Saleem Mufti ◽  
Muhammad Faisal Nadeem ◽  
Wei Gao ◽  
Zaheer Ahmad
Keyword(s):  
Molecular Structure ◽  
Real Number ◽  
Chemical Structure ◽  
Topological Index ◽  
Line Graph ◽  
Chemical Properties ◽  
Topological Indices ◽  
Molecular Structures ◽  
Line Graphs ◽  
Graph Invariant

AbstractA topological index is a map from molecular structure to a real number. It is a graph invariant and also used to describe the physio-chemical properties of the molecular structures of certain compounds. In this paper, we have investigated a chemical structure of pentacene. Our paper reflects the work on the following indices:Rα, Mα, χα, ABC, GA, ABC4, GA5, PM1, PM2, M1(G, p)and M1(G, p) of the para-line graph of linear [n]-pentacene and multiple pentacene.

scholarly journals F-Index of some graph operations

2016 ◽  
Vol 08 (02) ◽  
pp. 1650025 ◽  
Author(s):  
Nilanjan De ◽  
Sk. Md. Abu Nayeem ◽  
Anita Pal
Keyword(s):  
Electron Energy ◽  
Topological Index ◽  
Zagreb Index ◽  
Zagreb Indices ◽  
Molecular Graphs ◽  
Basic Properties ◽  
Graph Operations ◽  
Physico Chemical ◽  
Vertex Degrees

The F-index of a graph is defined as the sum of cubes of the vertex degrees of the graph. This was introduced in 1972, in the same paper where the first and second Zagreb indices were introduced to study the structure-dependency of total [Formula: see text]-electron energy. But this topological index was not further studied till then. Very recently, Furtula and Gutman [A forgotten topological index,J. Math. Chem. 53(4) (2015) 1184–1190.] reinvestigated the index and named it “forgotten topological index” or “F-index”. In that paper, they present some basic properties of this index and showed that this index can enhance the physico-chemical applicability of Zagreb index. Here, we study the behavior of this index under several graph operations and apply our results to find the F-index of different chemically interesting molecular graphs and nanostructures.

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