Forgotten Coindex for the Derived Sum Graphs under Cartesian Product

A topological index (TI) is a molecular descriptor that is applied on a chemical structure to compute the associated numerical value which measures volume, density, boiling point, melting point, surface tension, or solubility of this structure. It is an efficient mathematical method in avoiding laboratory experiments and time-consuming. The forgotten coindex of a structure or (molecular) graph H is defined as the sum of the degrees of all the possible pairs of nonadjacent vertices in H . For D ∈ S , R , Q , T and the connected graph H , the derived graphs D H are obtained by applying the operations S (subdivided), R (triangle parallel), Q (line superposition), and T (total graph), respectively. Moreover, a derived sum graph ( D -sum graph) is obtained by the Cartesian product of the graph H 2 with the graph D H 1 . In this study, we compute forgotten coindex of the D -sum graphs H 1 + S H 2 ( S -sum), H 1 + R H 2 ( R -sum), H 1 + Q H 2 ( Q -sum), and H 1 + T H 2 ( T -sum) in the form of various indices and coindices of the factor graphs H 1 and H 2 . At the end, we have analyzed our results using numerical tables and graphical behaviour for some particular D -sum graphs.

Download Full-text

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.

Download Full-text

The Second Hyper-Zagreb Coindex of Chemical Graphs and Some Applications

Journal of Chemistry ◽

10.1155/2021/3687533 ◽

2021 ◽

Vol 2021 ◽

pp. 1-8

Author(s):

Ahmed Ayache ◽

Abdu Alameri ◽

Mohammed Alsharafi ◽

Hanan Ahmed

Keyword(s):

Tensor Product ◽

Topological Index ◽

Molecular Graph ◽

Cartesian Product ◽

Explicit Formulas ◽

Chemical Graph ◽

Strong Product ◽

Chemical Graphs ◽

Product Composition ◽

Graph Structures

The second hyper-Zagreb coindex is an efficient topological index that enables us to describe a molecule from its molecular graph. In this current study, we shall evaluate the second hyper-Zagreb coindex of some chemical graphs. In this study, we compute the value of the second hyper-Zagreb coindex of some chemical graph structures such as sildenafil, aspirin, and nicotine. We also present explicit formulas of the second hyper-Zagreb coindex of any graph that results from some interesting graphical operations such as tensor product, Cartesian product, composition, and strong product, and apply them on a q-multiwalled nanotorus.

Download Full-text

A Survey of Quantitative Descriptions of Molecular Structure

Current Topics in Medicinal Chemistry ◽

10.2174/1568026611212180002 ◽

2013 ◽

Vol 12 (18) ◽

pp. 1946-1956 ◽

Cited By ~ 1

Author(s):

Rajarshi Guha ◽

Egon Willighagen

Keyword(s):

Molecular Structure ◽

Chemical Structure ◽

Computational Analysis ◽

Molecular Descriptor ◽

Molecular Graph ◽

Molecular Surface ◽

Numerical Characterization ◽

Numerical Representations ◽

Simple Atom

Numerical characterization of molecular structure is a first step in many computational analysis of chemical structure data. These numerical representations, termed descriptors, come in many forms, ranging from simple atom counts and invariants of the molecular graph to distribution of properties, such as charge, across a molecular surface. In this article we first present a broad categorization of descriptors and then describe applications and toolkits that can be employed to evaluate them. We highlight a number of issues surrounding molecular descriptor calculations such as versioning and reproducibility and describe how some toolkits have attempted to address these problems.

Download Full-text

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

Biointerface Research in Applied Chemistry ◽

10.33263/briac126.72497266 ◽

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.

Download Full-text

VDB Analysis for Zeolites LTA Structures

Biointerface Research in Applied Chemistry ◽

10.33263/briac125.69606977 ◽

2021 ◽

Vol 12 (5) ◽

pp. 6960-6977

Keyword(s):

Computer Simulations ◽

Chemical Structure ◽

Topological Index ◽

Chemical Properties ◽

Commercial Production ◽

Discovery Process ◽

Entropy Measures ◽

Analytical Expressions ◽

Significant Chemical ◽

Molecular Compounds

A distinct number used to characterize a molecular graph's chemical structure and significant chemical properties is a topological index. Quite a number of Vertex degree-based (VDB) indices have been introduced to investigate the structure of molecular compounds. Zeolites are a widely used family of aluminosilicates that have applications in chemistry, medicine, and commercial production due to their advantageous chemical properties. To aid in their creation, computer simulations have found millions of possible specific structures for zeolites. However, only a small percentage of these structures have been created. To aid in this discovery process, we extend the literature by computing the analytical expressions of VDB indices, VDB entropy measures, and VDB irregularity indices.

Download Full-text

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.

Download Full-text

Hosoya and Harary Polynomials of TOX(n),RTOX(n),TSL(n) and RTSL(n)

Discrete Dynamics in Nature and Society ◽

10.1155/2019/8696982 ◽

2019 ◽

Vol 2019 ◽

pp. 1-18 ◽

Cited By ~ 1

Author(s):

Lian Chen ◽

Abid Mehboob ◽

Haseeb Ahmad ◽

Waqas Nazeer ◽

Muhammad Hussain ◽

...

Keyword(s):

Topological Index ◽

Molecular Descriptor ◽

Wiener Index ◽

Vital Role ◽

Harary Index ◽

Chemical Graph ◽

Chemical Graph Theory ◽

Hosoya Polynomial ◽

Molecular Branching ◽

Path Number

In the fields of chemical graph theory, topological index is a type of a molecular descriptor that is calculated based on the graph of a chemical compound. In 1947, Wiener introduced “path number” which is now known as Wiener index and is the oldest topological index related to molecular branching. Hosoya polynomial plays a vital role in determining Wiener index. In this report, we computed the Hosoya and the Harary polynomials for TOX(n),RTOX(n),TSL(n), and RTSL(n) networks. Moreover, we computed serval distance based topological indices, for example, Wiener index, Harary index, and multiplicative version of wiener index.

Download Full-text

Fabrication of New Demulsifiers Employing the Waste Polyethylene Terephthalate and their Demulsification Efficiency for Heavy Crude Oil Emulsions

Molecules ◽

10.3390/molecules26030589 ◽

2021 ◽

Vol 26 (3) ◽

pp. 589

Author(s):

Mahmood M. S. Abdullah ◽

Hamad A. Al-Lohedan ◽

Ayman M. Atta

Keyword(s):

Surface Tension ◽

Light Scattering ◽

Polyethylene Terephthalate ◽

Chemical Structure ◽

Heavy Crude Oil ◽

Structure Surface ◽

Waste Polyethylene ◽

Heavy Crude ◽

Oil Emulsions ◽

Demulsification Efficiency

Two novel amphiphilic polyethylene amine terephthalate have been prepared via the glycolsis of polyethylene terephthalate (PET). The product, bis (2-hydroxyethyl terephthalate) (BHET), was converted to the corresponding dialkyl halide, bis(2-chloroethyl) terephthalate (BCET), using thionyl chloride (TC). This dialkyl compound was used for alkylation of dodecyl amine (DOA) and tetraethylenepentamine (TEPA) or pentaethylenehexamine (PEHA) to form the corresponding polyethylene amine terephthalate, i.e., DOAT and DOAP, respectively. Their chemical structure, surface tension, interfacial tension (IFT), and dynamic light scattering (DLS) were determined using different techniques. The efficiency of the prepared polyethylene amine terephthalate to demulsify water in heavy crude (W/O) emulsions was also determined and found to increase as their concentrations increased. Moreover, DOAT showed faster and higher efficiency, and cleaner separation than DOAP.

Download Full-text

Relating the ABC and harmonic indices

Journal of the Serbian Chemical Society ◽

10.2298/jsc130930001g ◽

2014 ◽

Vol 79 (5) ◽

pp. 557-563 ◽

Cited By ~ 4

Author(s):

Ivan Gutman ◽

Lingping Zhong ◽

Kexiang Xu

Keyword(s):

Molecular Structure ◽

Topological Index ◽

Molecular Graph ◽

Vertex Degree ◽

Harmonic Index ◽

Abc Index ◽

Atom Bond ◽

Structure Descriptor

The atom-bond connectivity (ABC) index is a much-studied molecular structure descriptor, based on the degrees of the vertices of the molecular graph. Recently, another vertex-degree-based topological index - the harmonic index (H) - attracted attention and gained popularity. We show how ABC and H are related.

Download Full-text