Computing Some Degree-Based Topological Indices of Honeycomb Networks

A topological index is a numeric quantity related with the chemical composition claiming to correlate the chemical structure with different chemical properties. Topological indices serve to predict physicochemical properties of chemical substance. Among different topological indices, degree-based topological indices would be helpful in investigating the anti-inflammatory activities of certain chemical networks. In the current study, we determine the neighborhood second Zagreb index and the first extended first-order connectivity index for oxide network O X n , silicate network S L n , chain silicate network C S n , and hexagonal network H X n . Also, we determine the neighborhood second Zagreb index and the first extended first-order connectivity index for honeycomb network H C n .

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Topological Characterization of Nanosheet Covered by C3 and C6

Processes ◽

10.3390/pr7070462 ◽

2019 ◽

Vol 7 (7) ◽

pp. 462

Author(s):

Sumiya Nasir ◽

Fozia Bashir Farooq ◽

Nazeran Idrees ◽

Muhammad Jawwad Saif ◽

Fatima Saeed

Keyword(s):

Chemical Structure ◽

Chemical Properties ◽

Topological Indices ◽

Connectivity Index ◽

Zagreb Index ◽

Topological Characterization ◽

Physical And Chemical ◽

Atom Bond ◽

And Chemical Properties

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 provides an alternate way to express the topological indices.

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Topological Indices of H-Naphtalenic Nanosheet

Open Chemistry ◽

10.1515/chem-2018-0131 ◽

2018 ◽

Vol 16 (1) ◽

pp. 1184-1188 ◽

Cited By ~ 2

Author(s):

Nazeran Idrees ◽

Muhammad Jawwad Saif ◽

Afshan Sadiq ◽

Asia Rauf ◽

Fida Hussain

Keyword(s):

Chemical Structure ◽

Topological Indices ◽

Connectivity Index ◽

First Zagreb Index ◽

Zagreb Index ◽

Chemical Graph ◽

Second Zagreb Index ◽

Topological Descriptor ◽

Chemical Graph Theory ◽

Atom Bond

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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Vertex-Based Topological Indices of Double and Strong Double Graph of Dutch Windmill Graph

Journal of Chemistry ◽

10.1155/2021/7057412 ◽

2021 ◽

Vol 2021 ◽

pp. 1-12

Author(s):

Muhammad Asad Ali ◽

Muhammad Shoaib Sardar ◽

Imran Siddique ◽

Dalal Alrowaili

Keyword(s):

Graph Theory ◽

Chemical Properties ◽

Topological Indices ◽

Connectivity Index ◽

Vaporization Enthalpy ◽

Zagreb Index ◽

Graph Operations ◽

Big Graphs ◽

Physical And Chemical ◽

Atom Bond

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

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

International Journal of Mathematics for Industry ◽

10.1142/s2661335219500060 ◽

2019 ◽

Vol 11 (01) ◽

pp. 1950006 ◽

Cited By ~ 2

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.

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On the Degree-Based Topological Indices of Some Derived Networks

Mathematics ◽

10.3390/math7070612 ◽

2019 ◽

Vol 7 (7) ◽

pp. 612 ◽

Cited By ~ 3

Author(s):

Haidar Ali ◽

Muhammad Ahsan Binyamin ◽

Muhammad Kashif Shafiq ◽

Wei Gao

Keyword(s):

Chemical Structure ◽

Chemical Properties ◽

Chemical Compounds ◽

Wiener Index ◽

Topological Indices ◽

Theoretical Chemistry ◽

Zagreb Index ◽

Entire Structure ◽

Physical Chemical ◽

Chemical Descriptors

There are numeric numbers that define chemical descriptors that represent the entire structure of a graph, which contain a basic chemical structure. Of these, the main factors of topological indices are such that they are related to different physical chemical properties of primary chemical compounds. The biological activity of chemical compounds can be constructed by the help of topological indices. In theoretical chemistry, numerous chemical indices have been invented, such as the Zagreb index, the Randić index, the Wiener index, and many more. Hex-derived networks have an assortment of valuable applications in drug store, hardware, and systems administration. In this analysis, we compute the Forgotten index and Balaban index, and reclassified the Zagreb indices, A B C 4 index, and G A 5 index for the third type of hex-derived networks theoretically.

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M-Polynomials and Topological Indices for Line Graphs of Chain Silicate Network and H-Naphtalenic Nanotubes

Journal of Mathematics ◽

10.1155/2021/5551825 ◽

2021 ◽

Vol 2021 ◽

pp. 1-11

Author(s):

Muhammad Irfan ◽

Hamood Ur Rehman ◽

Hassan Almusawa ◽

Saffina Rasheed ◽

Imran Abbas Baloch

Keyword(s):

Graph Theory ◽

Topological Index ◽

Chemical Properties ◽

Topological Indices ◽

Line Graphs ◽

Silicate Network ◽

Chemical Graph ◽

Chain Silicate

Graph theory has provided a very useful tool, called topological index, which is a number from the graph M with the property that every graph N isomorphic to M value of a topological index must be same for both M and N. Topological index is a descriptor in graph theory which is used to quantify the physio-chemical properties of the chemical graph. In this paper, we computed closed forms of M-polynomials for line graphs of H-naphtalenic nanotubes and chain silicate network. From M-polynomial, we obtained some topological indices based on degrees.

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Topological Indices of mth Chain Silicate Graphs

Mathematics ◽

10.3390/math7010042 ◽

2019 ◽

Vol 7 (1) ◽

pp. 42 ◽

Cited By ~ 2

Author(s):

Jia-Bao Liu ◽

Muhammad Kashif Shafiq ◽

Haidar Ali ◽

Asim Naseem ◽

Nayab Maryam ◽

...

Keyword(s):

Biological Activity ◽

Chemical Structure ◽

Chemical Properties ◽

Chemical Compounds ◽

Topological Indices ◽

Numerical Representation ◽

Topological Descriptor ◽

Physico Chemical ◽

Chain Silicate ◽

Atom Bond

A topological index is a numerical representation of a chemical structure, while a topological descriptor correlates certain physico-chemical characteristics of underlying chemical compounds besides its numerical representation. A large number of properties like physico-chemical properties, thermodynamic properties, chemical activity, and biological activity are determined by the chemical applications of graph theory. The biological activity of chemical compounds can be constructed by the help of topological indices such as atom-bond connectivity (ABC), Randić, and geometric arithmetic (GA). In this paper, Randić, atom bond connectivity (ABC), Zagreb, geometric arithmetic (GA), ABC4, and GA5 indices of the mth chain silicate S L ( m , n ) network are determined.

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Topological Indices of the Pent-Heptagonal Nanosheets VC5C7 and HC5C7

Advances in Materials Science and Engineering ◽

10.1155/2019/9594549 ◽

2019 ◽

Vol 2019 ◽

pp. 1-12

Author(s):

Fei Deng ◽

Xiujun Zhang ◽

Mehdi Alaeiyan ◽

Abid Mehboob ◽

Mohammad Reza Farahani

Keyword(s):

Topological Indices ◽

Connectivity Index ◽

First Zagreb Index ◽

Zagreb Index ◽

Second Zagreb Index ◽

Randić Connectivity Index ◽

Augmented Zagreb Index ◽

Forgotten Index ◽

Atom Bond ◽

Modified Zagreb Index

In this paper, we computed the topological indices of pent-heptagonal nanosheet. Formulas for atom-bond connectivity index, fourth atom-bond connectivity index, Randić connectivity index, sum-connectivity index, first Zagreb index, second Zagreb index, augmented Zagreb index, modified Zagreb index, hyper Zagreb index, geometric-arithmetic index, fifth geometric-arithmetic index, Sanskruti index, forgotten index, and harmonic index of pent-heptagonal nanosheet have been derived.

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Topological Indices of Vitamin D3

International Journal of Engineering & Technology ◽

10.14419/ijet.v7i4.24064 ◽

2018 ◽

Vol 7 (4) ◽

pp. 6276

Author(s):

Rajesh Kanna ◽

Roopa S ◽

PARASHIVAMURTHY H L

Keyword(s):

Vitamin D3 ◽

Topological Index ◽

Topological Indices ◽

Connectivity Index ◽

First Zagreb Index ◽

Zagreb Index ◽

Second Zagreb Index ◽

Augmented Zagreb Index ◽

Abc Index ◽

Ga Index

Graph theory has provided chemists with a variety of useful tools, such as topological indices. A topological index Top(G) of a graph G is a number with the property that for every graph H isomorphic to G, Top(H) = Top(G). In this paper, we compute ABC index, ABC4 index, Randi´c connectivity index, Sum connectivity index, GA index , GA5 index, First Zagreb index, Second Zagreb index, First Multiple Zagreb index, Second Multiple Zagreb index, Augmented Zagreb index, Harmonic index and Hyper Zagreb index, First Zagreb polynomial, Second Zagreb polynomial, Third Zagreb polynomial, Forgotten polynomials, Forgotten topological index and Symmetric division index of vitamin D3.

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Degree-Based Topological Indices of Boron B12

Journal of Chemistry ◽

10.1155/2021/5563218 ◽

2021 ◽

Vol 2021 ◽

pp. 1-6

Author(s):

Nouman Saeed ◽

Kai Long ◽

Zeeshan Saleem Mufti ◽

Hafsa Sajid ◽

Abdul Rehman

Keyword(s):

Chemical Structure ◽

Chemical Reactivity ◽

Molecular Descriptor ◽

Topological Indices ◽

Connectivity Index ◽

Melting Points ◽

Zagreb Index ◽

Boiling Points ◽

Electronic Parameters ◽

Atom Bond

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 Zagreb index, the general sum connectivity index, hyper-Zagreb index (HM), the atom-bond connectivity index (ABC), the geometric-arithmetic index (GA), the harmonic index (H), and the forgotten index (F).

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