scholarly journals On R degrees of vertices and R indices of graphs

2017 ◽  
Vol 5 (2) ◽  
pp. 70
Author(s):  
Süleyman Ediz
Keyword(s):  
Connected Graph ◽  
Chemical Properties ◽  
Topological Indices ◽  
Complete Graphs ◽  
Structure Property ◽  
Connected Graphs ◽  
Structure Activity ◽  
Structure Property Relationship ◽  
Simple Connected Graph ◽  
And Chemical Properties

Topological indices have been used to modeling biological and chemical properties of molecules in quantitive structure property relationship studies and quantitive structure activity studies. All the degree based topological indices have been defined via classical degree concept. In this paper we define a novel degree concept for a vertex of a simple connected graph: R degree. And also we define R indices of a simple connected graph by using the R degree concept. We compute the R indices for well-known simple connected graphs such as paths, stars, complete graphs and cycles.

scholarly journals On S Degrees of Vertices and S Indices of Graphs

2017 ◽  
Author(s):  
Süleyman Ediz
Keyword(s):  
Connected Graph ◽  
Chemical Properties ◽  
Topological Indices ◽  
Complete Graphs ◽  
Structure Property ◽  
Connected Graphs ◽  
Structure Activity ◽  
Structure Property Relationship ◽  
Simple Connected Graph ◽  
And Chemical Properties

Topological indices have been used to modeling biological and chemical properties of molecules in quantitive structure property relationship studies and quantitive structure activity studies. All the degree based topological indices have been defined via classical degree concept. In this paper we define a novel degree concept for a vertex of a simple connected graph: S degree. And also we define S indices of a simple connected graph by using the S degree concept. We compute the S indices for well-known simple connected graphs such as paths, stars, complete graphs and cycles.

ON MOSTAR INDEX OF GRAPHS

2021 ◽  
Vol 10 (4) ◽  
pp. 2115-2129
Author(s):  
P. Kandan ◽  
S. Subramanian
Keyword(s):  
Connected Graph ◽  
Cartesian Product ◽  
Bipartite Graphs ◽  
Topological Indices ◽  
Great Success ◽  
Complete Graphs ◽  
Molecular Graphs ◽  
Graphs And Networks ◽  
Complete Bipartite Graphs ◽  
Simple Connected Graph

On the great success of bond-additive topological indices like Szeged, Padmakar-Ivan, Zagreb, and irregularity measures, yet another index, the Mostar index, has been introduced recently as a peripherality measure in molecular graphs and networks. For a connected graph G, the Mostar index is defined as $$M_{o}(G)=\displaystyle{\sum\limits_{e=gh\epsilon E(G)}}C(gh),$$ where $C(gh) \,=\,\left|n_{g}(e)-n_{h}(e)\right|$ be the contribution of edge $uv$ and $n_{g}(e)$ denotes the number of vertices of $G$ lying closer to vertex $g$ than to vertex $h$ ($n_{h}(e)$ define similarly). In this paper, we prove a general form of the results obtained by $Do\check{s}li\acute{c}$ et al.\cite{18} for compute the Mostar index to the Cartesian product of two simple connected graph. Using this result, we have derived the Cartesian product of paths, cycles, complete bipartite graphs, complete graphs and to some molecular graphs.

scholarly journals Topological indices of rhombus type silicate and oxide networks

2017 ◽  
Vol 95 (2) ◽  
pp. 134-143 ◽  
Author(s):  
M. Javaid ◽  
Masood Ur Rehman ◽  
Jinde Cao
Keyword(s):  
Molecular Graph ◽  
Chemical Compounds ◽  
Quantitative Structure Activity Relationship ◽  
Topological Indices ◽  
Quantitative Structure ◽  
Structure Property ◽  
Structure Activity ◽  
Structure Property Relationship ◽  
Cartesian Coordinate ◽  
Atom Bond

For a molecular graph, a numeric quantity that characterizes the whole structure of a graph is called a topological index. In the studies of quantitative structure – activity relationship (QSAR) and quantitative structure – property relationship (QSPR), topological indices are utilized to guess the bioactivity of chemical compounds. In this paper, we compute general Randić, first general Zagreb, generalized Zagreb, multiplicative Zagreb, atom-bond connectivity (ABC), and geometric arithmetic (GA) indices for the rhombus silicate and rhombus oxide networks. In addition, we also compute the latest developed topological indices such as the fourth version of ABC (ABC4), the fifth version of GA (GA5), augmented Zagreb, and Sanskruti indices for the foresaid networks. At the end, a comparison between all the indices is included, and the result is shown with the help of a Cartesian coordinate system.

scholarly journals Microscopy and Microanalysis of Nano-Scale Materials

2006 ◽  
Vol 14 (5) ◽  
pp. 6-15 ◽  
Author(s):  
J. R. Michael ◽  
L. N. Brewer ◽  
D. C. Miller ◽  
K. R. Zavadil ◽  
S. V. Prasad ◽  
...  
Keyword(s):  
Chemical Properties ◽  
Structure Property ◽  
Length Scales ◽  
Full Characterization ◽  
Microelectronic Devices ◽  
Structure Property Relationship ◽  
Scientists And Engineers ◽  
Physical And Chemical ◽  
And Chemical Properties

Material scientists and engineers continue to developmaterials and structures that are ever smaller. Some of this engineering is to simply domore with less while the science of nanomaterials allows new materials to be produced with a novel range of physical and chemical properties due to the small length scales of the microstructural features of thematerials. Currently, nanoscalematerials have been produced with a diverse set of useful properties and can be found in common substances like sunscreen or technologically advanced microelectronic devices. A complete understanding of materials is based on knowledge of the processing used to produce an interesting material coupled with a full characterization of the structure that results. It is this structure/property relationship that is the basis of understanding any newmaterial developed at all length scales.

scholarly journals M-Polynomials and Degree-Based Topological Indices of the Crystallographic Structure of Molecules

Biomolecules ◽  
2018 ◽  
Vol 8 (4) ◽  
pp. 107 ◽  
Author(s):  
Wei Gao ◽  
Muhammad Younas ◽  
Adeel Farooq ◽  
Abid Mahboob ◽  
Waqas Nazeer
Keyword(s):  
Strain Energy ◽  
Chemical Properties ◽  
Quantitative Structure Activity Relationship ◽  
Topological Indices ◽  
Crystallographic Structure ◽  
Physical And Chemical Properties ◽  
Structure Of Molecules ◽  
Structure Activity ◽  
Physical And Chemical ◽  
And Chemical Properties

Topological indices are numerical parameters used to study the physical and chemical properties of compounds. In quantitative structure–activity relationship QSARs, topological indices correlate the biological activity of compounds with their physical properties like boiling point, stability, melting point, distortion, and strain energy etc. In this paper, we determined the M-polynomials of the crystallographic structure of the molecules Cu2O and TiF2 [p,q,r]. Then we derived closed formulas for some well-known topological indices using calculus. In the end, we used Maple 15 to plot surfaces associated with the topological indices of Cu2O and TiF2 [p,q,r].

scholarly journals Some Topological Measures for Nicotine

2020 ◽  
pp. 287-296
Author(s):  
Abaid ur Rehman Virk
Keyword(s):  
Topological Index ◽  
Chemical Properties ◽  
Chemical Compounds ◽  
Physical And Chemical Properties ◽  
Quantitative Structure ◽  
Structure Property ◽  
Structure Property Relationship ◽  
Topological Measures ◽  
Physical And Chemical ◽  
And Chemical Properties

A topological index is a quantity expressed as a number that help us to catch symmetry of chemical compounds. With the help of quantitative structure property relationship (QSPR), we can guess physical and chemical properties of several chemical compounds. Here, we will compute Shingali & Kanabour, Gourava and hype Gourava indices for the chemical compound Nicotine.

scholarly journals On Topological Indices for New Classes of Benes Network

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Aftab Hussain ◽  
Muhammad Numan ◽  
Nafisa Naz ◽  
Saad Ihsan Butt ◽  
Adnan Aslam ◽  
...  
Keyword(s):  
Molecular Graph ◽  
Quantitative Structure Activity Relationship ◽  
Topological Indices ◽  
Structure Property ◽  
Structure Activity ◽  
Randić Connectivity Index ◽  
Structure Property Relationship ◽  
Benes Network ◽  
Benes Networks ◽  
Atom Bond

Topological indices (TIs) transform a molecular graph into a number. The TIs are a vital tool for quantitative structure activity relationship (QSAR) and quantity structure property relationship (QSPR). In this paper, we constructed two classes of Benes network: horizontal cylindrical Benes network HCB r and vertical cylindrical Benes network obtained by identification of vertices of first rows with last row and first column with last column of Benes network, respectively. We derive analytical close formulas for general Randić connectivity index, general Zagreb, first and the second Zagreb (and multiplicative Zagreb), general sum connectivity, atom-bond connectivity ( VCB r ), and geometric arithmetic ABC index of the two classes of Benes networks. Also, the fourth version of GA and the fifth version of ABC indices are computed for these classes of networks.

scholarly journals Computation of certain topological coindices of graphene sheet and C4C8(S) nanotubes and nanotorus

2019 ◽  
Vol 4 (2) ◽  
pp. 455-468 ◽  
Author(s):  
Melaku Berhe ◽  
Chunxiang Wang
Keyword(s):  
Graphene Sheet ◽  
Biological Activities ◽  
Chemical Properties ◽  
Quantitative Structure Activity Relationship ◽  
Topological Indices ◽  
Quantitative Structure ◽  
Structure Property ◽  
Structure Property Relationship ◽  
Relationship Of ◽  
The Relationship

AbstractTopological indices are widely used for quantitative structure-activity relationship (QSAR) and quantitative structure-property relationship (QSPR). Topological coindices are topological indices that considers the non adjacent pairs of vertices. Here, we consider the following five well-known topological coindices: the first and second Zagreb coindices, the first and second multiplicative Zagreb coindices and the F-coindex. By using graph structural analysis and derivation, we study the above-mentioned topological coindices of some chemical molecular graphs that frequently appear in medical, chemical, and material engineering such as graphene sheet and C4C8(S) nanotubes and nanotorus and obtain the computation formulae of the coindices of these graphs. Furthermore, we analyze the results by MATLAB and obtain the relationship of the coindices which they describe the physcio-chemical properties and biological activities.

scholarly journals Minimum Detour Index of Tricyclic Graphs

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Wei Fang ◽  
Zheng-Qun Cai ◽  
Xiao-Xin Li
Keyword(s):  
Connected Graph ◽  
Quantitative Structure Activity Relationship ◽  
Activity Relationship ◽  
Quantitative Structure ◽  
Structure Property ◽  
Quantitative Structure Property Relationship ◽  
Structure Activity ◽  
Structure Property Relationship ◽  
Longest Paths ◽  
Tricyclic Graphs

The detour index of a connected graph is defined as the sum of the detour distances (lengths of longest paths) between unordered pairs of vertices of the graph. The detour index is used in various quantitative structure-property relationship and quantitative structure-activity relationship studies. In this paper, we characterize the minimum detour index among all tricyclic graphs, which attain the bounds.

scholarly journals M-Polynomials and Topological Indices of Titania Nanotubes

2016 ◽  
Author(s):  
Shin Min Kang ◽  
Mobeen Munir ◽  
Abdul Rauf Nizami ◽  
Shazia Rafique ◽  
Waqas Nazeer
Keyword(s):  
Tio2 Nanotubes ◽  
Strain Energy ◽  
Gas Sensing ◽  
Chemical Properties ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Structure Activity ◽  
Different Types ◽  
Quantitative Structure Activity Relationships ◽  
And Chemical Properties

Titania is one of the most comprehensively studied nanostructures due to its widespread applications in production of catalytic, gas- sensing and corrosion- resistance materials [1]. M-polynomial of nanotubes has been vastly investigated as it produces many degree-based topological indices which are numerical parameters capturing structural and chemical properties. These indices are used in the development of quantitative structure-activity relationships (QSARs) in which the biological activity and other properties of molecules are correlated with their structure like boiling point, stability, strain energy etc of chemical compounds. In this paper, we determine M-polynomials of single-walled titanium (SW TiO2) nanotubes and recover important topological degree based indices of them to theoretically judge these nanotubes. We also use Maple to plot surfaces associated to different types of single-walled titanium (SW TiO2) nanotubes.

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