scholarly journals Second Atom-Bond Connectivity Index of Special Chemical Molecular Structures

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Wei Gao ◽  
Weifan Wang
Keyword(s):  
Strain Energy ◽  
Theoretical Chemistry ◽  
Molecular Structures ◽  
Connectivity Index ◽  
Hexagonal Chain ◽  
Polyomino Chain ◽  
The Stability ◽  
Atom Bond

In theoretical chemistry, the second atom-bond connectivity index was introduced to measure the stability of alkanes and the strain energy of cycloalkanes. In this paper, we determine the second atom-bond connectivity index of unilateral polyomino chain and unilateral hexagonal chain. Furthermore, the secondABCindices of V-phenylenic nanotubes and nanotori are presented.

scholarly journals The first multiplication atom-bond connectivity index of molecular structures in drugs

2017 ◽  
Vol 25 (4) ◽  
pp. 548-555 ◽  
Author(s):  
Wei Gao ◽  
Yiqiao Wang ◽  
Weifan Wang ◽  
Li Shi
Keyword(s):  
Molecular Structures ◽  
Connectivity Index ◽  
Atom Bond

The eccentric version of atom-bond connectivity index of tetra sheet networks

2018 ◽  
Vol 10 (05) ◽  
pp. 1850065 ◽  
Author(s):  
Muhammad Imran ◽  
Abdul Qudair Baig ◽  
Muhammad Razwan Azhar
Keyword(s):  
Connected Graph ◽  
Molecular Graph ◽  
Theoretical Chemistry ◽  
Connectivity Index ◽  
Maximum Distance ◽  
Eccentric Connectivity Index ◽  
Topological Descriptor ◽  
Degree Of A Vertex ◽  
Connectivity Indices ◽  
Atom Bond

Among topological descriptor of graphs, the connectivity indices are very important and they have a prominent role in theoretical chemistry. The atom-bond connectivity index of a connected graph [Formula: see text] is represented as [Formula: see text], where [Formula: see text] represents the degree of a vertex [Formula: see text] of [Formula: see text] and the eccentric connectivity index of the molecular graph [Formula: see text] is represented as [Formula: see text], where [Formula: see text] is the maximum distance between the vertex [Formula: see text] and any other vertex [Formula: see text] of the graph [Formula: see text]. The new eccentric atom-bond connectivity index of any connected graph [Formula: see text] is defined as [Formula: see text]. In this paper, we compute the new eccentric atom-bond connectivity index for infinite families of tetra sheets equilateral triangular and rectangular networks.

scholarly journals On molecular topological properties of benzenoid structures

2016 ◽  
Vol 94 (8) ◽  
pp. 687-698 ◽  
Author(s):  
Shehnaz Akhter ◽  
Muhammad Imran
Keyword(s):  
Strain Energy ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Connectivity Index ◽  
Line Graphs ◽  
Zigzag Edge ◽  
Zagreb Index ◽  
Chemical Significance ◽  
Randić Connectivity Index ◽  
Atom Bond

The degree-based topological indices correlate certain physicochemical properties such as boiling point, strain energy, and stability, etc., of certain chemical compounds. Among the major classes of topological indices are the distance-based topological indices, degree-based topological indices, and counting-related polynomials and corresponding indices of graphs. Among all of the degree-based indices, namely the first general Zagreb index, general Rndić connectivity index, general sum-connectivity index, atom–bond connectivity index (ABC), and geometric–arithmetic index (GA), are most important due to their chemical significance. In this paper, we compute the first general Zagreb index, general Randić connectivity index, general sum-connectivity index, ABC, GA, ABC4, and GA5 indices of hexagonal parallelogram P(m,n) nanotubes, triangular benzenoid Gn, and zigzag-edge coronoid fused with starphene ZCS(k,l,m) nanotubes by using the line graphs of the subdivision of these chemical graphs.

scholarly journals Some inequalities for the atom-bond connectivity index of graph operations

2011 ◽  
Vol 159 (13) ◽  
pp. 1323-1330 ◽  
Author(s):  
G.H. Fath-Tabar ◽  
B. Vaez-Zadeh ◽  
A.R. Ashrafi ◽  
A. Graovac
Keyword(s):  
Connectivity Index ◽  
Graph Operations ◽  
Atom Bond

scholarly journals On Atom-Bond Connectivity Index

2011 ◽  
Vol 66a ◽  
pp. 61 ◽  
Author(s):  
Zhou B. ◽  
Xing R.
Keyword(s):  
Connectivity Index ◽  
Atom Bond

scholarly journals More on comparison between first geometric-arithmetic index and atom-bond connectivity index

2016 ◽  
Vol 17 (1) ◽  
pp. 561 ◽  
Author(s):  
Zahid Raza ◽  
Akhlaq Ahmad Bhatti ◽  
Akbar Ali
Keyword(s):  
Connectivity Index ◽  
Atom Bond

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

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 .

scholarly journals Some Eccentricity-Based Topological Indices and Polynomials of Poly(EThyleneAmidoAmine) (PETAA) Dendrimers

Processes ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 433 ◽  
Author(s):  
Jialin Zheng ◽  
Zahid Iqbal ◽  
Asfand Fahad ◽  
Asim Zafar ◽  
Adnan Aslam ◽  
...  
Keyword(s):  
Molecular Descriptors ◽  
Molecular Graph ◽  
Topological Indices ◽  
Molecular Structures ◽  
Connectivity Index ◽  
Connectivity Indices ◽  
Numerical Invariants ◽  
Explicit Representations ◽  
Pharmaceutical Properties

Topological indices have been computed for various molecular structures over many years. These are numerical invariants associated with molecular structures and are helpful in featuring many properties. Among these molecular descriptors, the eccentricity connectivity index has a dynamic role due to its ability of estimating pharmaceutical properties. In this article, eccentric connectivity, total eccentricity connectivity, augmented eccentric connectivity, first Zagreb eccentricity, modified eccentric connectivity, second Zagreb eccentricity, and the edge version of eccentric connectivity indices, are computed for the molecular graph of a PolyEThyleneAmidoAmine (PETAA) dendrimer. Moreover, the explicit representations of the polynomials associated with some of these indices are also computed.

Evaluation of the Stability of Raft Structure in Nickel Base Superalloys Throughout their Lifetime

2006 ◽  
Vol 980 ◽  
Author(s):  
Katsushi Tanaka ◽  
Toru Inoue ◽  
Tetsu Ichitsubo ◽  
Kyosuke Kishida ◽  
Haruyuki Inui
Keyword(s):  
Strain Energy ◽  
Lattice Misfit ◽  
Gamma Prime ◽  
Lamellar Interface ◽  
Nickel Base Superalloys ◽  
Nickel Base ◽  
The Stability ◽  
Numerical Calculation Method ◽  
Creep Deformations ◽  
Lamellar Interfaces

AbstractStability of raft structure in nickel base superalloys has been examined by using elastic energy calculations based on a microelasticity theory. The numerical calculation method for a structurally heterogeneous system is applied. The results indicate that the raft structure is significantly stabilized by introductions of creep deformations till the critical creep deformation at which the lattice misfit between gamma and gamma-prime phases is completely compensated by creep dislocations. When the magnitude of creep deformations exceed the critical value, the (001) lamellar interfaces become elastically unstable and a tilted lamellar interface become the most stable one. This instability of the 001 raft structure leads a tilted or wavy lamellar interfaces for reducing the internal strain energy, that is a precursor to collapse the raft structure.

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