Molecular Descriptors of Nanotube, Oxide, Silicate, and Triangulene 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.

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On topological properties of block shift and hierarchical hypercube networks

Open Physics ◽

10.1515/phys-2018-0101 ◽

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).

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On topological indices of a carbon nanotube network

Canadian Journal of Chemistry ◽

10.1139/cjc-2015-0175 ◽

2015 ◽

Vol 93 (10) ◽

pp. 1157-1160 ◽

Cited By ~ 32

Author(s):

Martin Bača ◽

Jarmila Horváthová ◽

Martina Mokrišová ◽

Andrea Semaničová-Feňovčíková ◽

Alžbeta Suhányiová

Keyword(s):

Carbon Nanotube ◽

Topological Index ◽

Hexagonal Lattice ◽

Topological Indices ◽

Important Class ◽

Chemical Graph ◽

Chemical Graph Theory ◽

Carbon Nanotube Network ◽

Vertex Degrees ◽

Atom Bond

A numerical quantity that characterizes the whole structure of a graph is called a topological index. The concept of Randić (Rα), atom−bond connectivity (ABC), and geometric−arithmetic (GA) topological indices was established in chemical graph theory based on vertex degrees. In this paper, we study a carbon nanotube network that is motivated by the molecular structure of a regular hexagonal lattice and determine Rα, ABC, and GA indices for this important class of networks.

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Reformulated Zagreb Indices of Some Derived Graphs

Mathematics ◽

10.3390/math7040366 ◽

2019 ◽

Vol 7 (4) ◽

pp. 366 ◽

Cited By ~ 6

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.

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The (a,b)-Zagreb index of line graphs of subdivision graphs of some molecular structures

International Journal of Mathematics for Industry ◽

10.1142/s2661335220500069 ◽

2020 ◽

pp. 1-9

Author(s):

Prosanta Sarkar ◽

Anita Pal ◽

Nilanjan De

Keyword(s):

Chemical Structure ◽

Molecular Structures ◽

Line Graphs ◽

Zagreb Index ◽

Physiochemical Properties ◽

Chemical Graph ◽

Chemical Structures ◽

Chemical Graph Theory ◽

Chemical Constitution ◽

Structure Descriptor

A graph is a mathematical model used to predict the topology of a given system. In chemical graph theory, a graph is designed by considering atoms as vertices and edges as bonds between atoms of a particular molecule. A topological index or molecular structure descriptor is a numeric quantity associated with the chemical constitution which correlated with various physiochemical properties of the chemical structure. In this paper, we study the [Formula: see text]-Zagreb index of line graphs of the subdivision graphs of some chemical structures.

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Topological Indices of Certain Transformed Chemical Structures

Journal of Chemistry ◽

10.1155/2020/3045646 ◽

2020 ◽

Vol 2020 ◽

pp. 1-7 ◽

Cited By ~ 1

Author(s):

Xuewu Zuo ◽

Jia-Bao Liu ◽

Hifza Iqbal ◽

Kashif Ali ◽

Syed Tahir Raza Rizvi

Keyword(s):

Carbon Nanotube ◽

Line Graph ◽

Topological Indices ◽

Connectivity Index ◽

Zagreb Index ◽

Harmonic Index ◽

Chemical Structures ◽

Augmented Zagreb Index ◽

Carbon Nanotube Networks ◽

Atom Bond

Topological indices like generalized Randić index, augmented Zagreb index, geometric arithmetic index, harmonic index, product connectivity index, general sum-connectivity index, and atom-bond connectivity index are employed to calculate the bioactivity of chemicals. In this paper, we define these indices for the line graph of k-subdivided linear [n] Tetracene, fullerene networks, tetracenic nanotori, and carbon nanotube networks.

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Ultrafast structural evolution and formation of linear carbon chains in single-walled carbon nanotube networks by femtosecond laser irradiation

Nanoscale ◽

10.1039/c7nr05883g ◽

2017 ◽

Vol 9 (43) ◽

pp. 16627-16631 ◽

Cited By ~ 4

Author(s):

Jeonghong Ha ◽

Hyun Young Jung ◽

Ji Hao ◽

Bo Li ◽

Aldo Raeliarijaona ◽

...

Keyword(s):

Molecular Structure ◽

Carbon Nanotube ◽

Femtosecond Laser ◽

Laser Irradiation ◽

Structural Evolution ◽

Femtosecond Laser Irradiation ◽

Single Walled Carbon Nanotube ◽

Single Walled Carbon ◽

Carbon Chains ◽

Carbon Nanotube Networks

This work demonstrates a method for engineering a molecular structure of single-walled carbon nanotube networks by femtosecond laser irradiation.

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Graphs with maximal irregularity

Filomat ◽

10.2298/fil1407315a ◽

2014 ◽

Vol 28 (7) ◽

pp. 1315-1322 ◽

Cited By ~ 18

Author(s):

Hosam Abdo ◽

Nathann Cohen ◽

Darko Dimitrov

Keyword(s):

Upper Bound ◽

Undirected Graph ◽

Graph Invariant ◽

Zagreb Index ◽

Second Zagreb Index ◽

Chemical Graph Theory ◽

Degree Of A Vertex ◽

Maximal Vertex ◽

Vertex Degrees ◽

General Graphs

Albertson [3] has defined the P irregularity of a simple undirected graph G = (V,E) as irr(G) =?uv?E |dG(u)- dG(v)|, where dG(u) denotes the degree of a vertex u ? V. Recently, this graph invariant gained interest in the chemical graph theory, where it occured in some bounds on the first and the second Zagreb index, and was named the third Zagreb index [12]. For general graphs with n vertices, Albertson has obtained an asymptotically tight upper bound on the irregularity of 4n3/27: Here, by exploiting a different approach than in [3], we show that for general graphs with n vertices the upper bound ?n/3? ?2n/3? (?2n/3? -1) is sharp. We also present lower bounds on the maximal irregularity of graphs with fixed minimal and/or maximal vertex degrees, and consider an approximate computation of the irregularity of a graph.

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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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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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