scholarly journals Wiener Index of Edge Thorny Graphs of Catacondensed Benzenoids

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 467
Author(s):  
Andrey A. Dobrynin ◽  
Ali Iranmanesh
Keyword(s):  
Polycyclic Aromatic Hydrocarbons ◽  
Aromatic Hydrocarbons ◽  
Topological Index ◽  
Perfect Matching ◽  
Molecular Graph ◽  
Wiener Index ◽  
Benzenoid Graph ◽  
Polycyclic Aromatic ◽  
Distance Properties ◽  
Sum Of Distances

The Wiener index is a topological index of a molecular graph, defined as the sum of distances between all pairs of its vertices. Benzenoid graphs include molecular graphs of polycyclic aromatic hydrocarbons. An edge thorny graph G is constructed from a catacondensed benzenoid graph H by attaching new graphs to edges of a perfect matching of H. A formula for the Wiener index of G is derived. The index of the resulting graph does not contain distance characteristics of elements of H and depends on the Wiener index of H and distance properties of the attached graphs.

Computing Analysis of Degree and Connection Based Irregular Indices of Polycyclic Aromatic Hydrocarbons

2021 ◽  
Vol 18 ◽  
Author(s):  
Muhammad Javaid ◽  
Muhammad Ibraheem ◽  
Abdul Raheem
Keyword(s):  
Polycyclic Aromatic Hydrocarbons ◽  
Aromatic Hydrocarbons ◽  
Topological Index ◽  
Medical Science ◽  
Molecular Graph ◽  
Chemical Compounds ◽  
Molecular Graphs ◽  
Equal Degree ◽  
Physical Chemical ◽  
Polycyclic Aromatic

Introduction: A graph is supposed to be regular if all vertices have equal degree, otherwise irregular. Materials and Methods: Polycyclic aromatic hydrocarbons are important combusting material and considered as class of carcinogens. These polycyclic aromatic hydrocarbons play an important role in graphitisation of medical science. A topological index is a function that assigns a numerical value to a (molecular) graph which predicts various physical, chemical, biological, thermodynamical and structural properties of (molecular) graphs. An irregular index is a topological index that measures the irregularity of atoms with respect to their bonding for the chemical compounds which are involved in the under studying graphs. Results and Discussion: In this paper, we will compute an analysis of distance based irregular indices of polycyclic aromatic hydrocarbons. A comparison among the obtained indices with the help of their numerical values and the 3D presentations is also included. The efficient and steady indices of polycyclic aromatic hydrocarbons are addressed in the form of their irregularities. Conclusion: Connection based study of the molecular graphs is more suitable than the degree based irregularity indices.

scholarly journals The General (α,3)-Path Connectivity Indices of Polycyclic Aromatic Hydrocarbons

2018 ◽  
Vol 2018 ◽  
pp. 1-5
Author(s):  
Haiying Wang ◽  
Chuantao Li
Keyword(s):  
Applied Sciences ◽  
Polycyclic Aromatic Hydrocarbons ◽  
Aromatic Hydrocarbons ◽  
Molecular Graph ◽  
Three Dimensional ◽  
3D Qsar ◽  
Medical Sciences ◽  
Connectivity Indices ◽  
Polycyclic Aromatic ◽  
Extremal Values

The general (α,t)-path connectivity index of a molecular graph originates from many practical problems such as three-dimensional quantitative structure-activity (3D QSAR) and molecular chirality. It is defined as Rtα(G)=∑Pt=vi1vi2⋯vit+1⊆G[d(vi1)d(vi2)⋯d(vit+1)]α, where the summation is taken over all possible paths of length t of G and we do not distinguish between the paths vi1vi2⋯vit+1 and vit+1⋯vi2vi1. In this paper, we focus on the structures of Polycyclic Aromatic Hydrocarbons (PAHn), which play a role in organic materials and medical sciences. We try to compute the exact general (α,3)-path connectivity indices of this family of hydrocarbon structures. Furthermore, we exactly derive the monotonicity and the extremal values of R3α(PAHn) for any real number α. These valuable results could produce strong guiding significance to these applied sciences.

scholarly journals Schultz and Modified Schultz Polynomials of Coronene Polycyclic Aromatic Hydrocarbons

2014 ◽  
Vol 32 ◽  
pp. 1-10
Author(s):  
Mohammad Reza Farahani
Keyword(s):  
Polycyclic Aromatic Hydrocarbons ◽  
Graph Theory ◽  
Shortest Path ◽  
Aromatic Hydrocarbons ◽  
Connected Graph ◽  
Molecular Graph ◽  
Hydrocarbon Molecule ◽  
Polycyclic Aromatic ◽  
Hosoya Polynomial ◽  
Simple Connected Graph

Let G = (V;E) be a simple connected graph. The sets of vertices and edges of G are denoted byV = V(G) and E = E(G), respectively. In such a simple molecular graph, vertices represent atoms andedges represent bonds. The distance between the vertices u and v in V(G) of graph G is the number ofedges in a shortest path connecting them, we denote by d(u,v). In graph theory, we have manyinvariant polynomials for a graph G. In this research, we computing the Schultz polynomial, ModifiedSchultz polynomial, Hosoya polynomial and their topological indices of a Hydrocarbon molecule, thatwe call “Coronene Polycyclic Aromatic Hydrocarbons”.

On Topology-Property Relations of Polycyclic Aromatic Hydrocarbons

1985 ◽  
Vol 40 (6) ◽  
pp. 636-638 ◽  
Author(s):  
M. Zander
Keyword(s):  
Polycyclic Aromatic Hydrocarbons ◽  
Aromatic Hydrocarbons ◽  
Topological Index ◽  
Chemical Reactivity ◽  
Molecular Topology ◽  
Property Relations ◽  
Resonance Energies ◽  
Polycyclic Aromatic ◽  
Theory And Experiments ◽  
Mo Theory

The hydrogen-depleted graphs of polycyclic aromatic hydrocarbons contain two types of vertices (with regard to their degree) and correspondingly three types of edges. The respective sums of these edges reflect the molecular topology of the hydrocarbons and were used for constructing a new topological index for kata-annellated aromatic hydrocarbons that correlates well with their topological resonance energies per electron. Dependent on the degrees of their first neighbours, the vertices of degree 2 of polycyclic hydrocarbons can be distinguished as to high, medium and low chemical reactivity of the corresponding carbon atoms, in agreement with the results from MO theory and experiments.

scholarly journals General (α,2)-Path Sum-Connectivirty Indices of One Important Class of Polycyclic Aromatic Hydrocarbons

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 426
Author(s):  
Haiying Wang
Keyword(s):  
Polycyclic Aromatic Hydrocarbons ◽  
Real Number ◽  
Aromatic Hydrocarbons ◽  
Molecular Graph ◽  
Three Dimensional ◽  
3D Qsar ◽  
Important Class ◽  
Polycyclic Aromatic ◽  
T Path ◽  
Extremal Values

The general ( α , t ) -path sum-connectivity index of a molecular graph originates from many practical problems, such as the three-dimensional quantitative structure–activity relationships (3D QSAR) and molecular chirality. For arbitrary nonzero real number α and arbitrary positive integer t, it is defined as t χ α ( G ) = ∑ P t = v i 1 v i 2 ⋯ v i t + 1 ⊆ G [ d G ( v i 1 ) d G ( v i 2 ) ⋯ d G ( v i t + 1 ) ] α , where we take the sum over all possible paths of length t of G and two paths v i 1 v i 2 ⋯ v i t + 1 and v i t + 1 ⋯ v i 2 v i 1 are considered to be one path. In this work, one important class of polycyclic aromatic hydrocarbons and their structures are firstly considered, which play a role in organic materials and medical sciences. We try to compute the exact general ( α , 2 ) -path sum-connectivity indices of these hydrocarbon systems. Furthermore, we exactly derive the monotonicity and the extremal values of these polycyclic aromatic hydrocarbons for any real number α . These valuable results could produce strong guiding significance to these applied sciences.

Topologische Indices alternierender polycyclischer aromatischer Kohlenwasserstoffe und ihre Korrelationen mit elektronischen Eigenschaften / Topological Indices of Alternant Polycyclic Aromatic Hydrocarbons and their Correlations with Electronic Properties

1981 ◽  
Vol 36 (11) ◽  
pp. 1217-1221
Author(s):  
K.-D. Gundermann ◽  
C. Lohberger ◽  
M. Zander
Keyword(s):  
Polycyclic Aromatic Hydrocarbons ◽  
Electronic Properties ◽  
Aromatic Hydrocarbons ◽  
Topological Index ◽  
Distance Matrix ◽  
Topological Indices ◽  
Matrix Elements ◽  
Wiener Number ◽  
Polycyclic Aromatic ◽  
Aromatic Systems

The half-sum of the distance matrix elements derived from the characteristic graphs, i.e. the Wiener number of these graphs is proposed as a new topological index for alternant polycyclic aromatic hydrocarbons. It is shown by regression analysis that correlations between topological indices and electronic properties of alternant aromatic systems do only exist for those indices and properties which depend to the same degree from the size of the systems and for which the corresponding relation applies to the topology.

scholarly journals The Theta polynomial Θ(G,x) and the Theta index Θ(G) of molecular graph Polycyclic Aromatic Hydrocarbons PAHk

2015 ◽  
Vol 12 (1) ◽  
pp. 3934-3939 ◽  
Author(s):  
Wei Gao ◽  
MOHAMMAD REZA FARAHANI
Keyword(s):  
Polycyclic Aromatic Hydrocarbons ◽  
Positive Integer ◽  
Aromatic Hydrocarbons ◽  
Molecular Graph ◽  
Integer Number ◽  
Polycyclic Aromatic ◽  
Omega Polynomial

The omega polynomial Ω(G,x), for counting qoc strips in molecular graph G was defined by Diudea as  with m(G,c), being the number of qoc strips of length c. The Theta polynomial Θ(G,x) and the Theta index Θ(G) of a molecular graph G were defined as Θ(G,x)= and Θ(G)=, respectively.In this paper, we compute the Theta polynomial Θ(G,x) and the Theta index Θ(G) of molecular graph Polycyclic Aromatic Hydrocarbons PAHk, for all positive integer number k. 

Computing a Closed Formula of the Wiener Index of the Polycyclic Aromatic Hydrocarbons PAHk by Using the Cut Method

2017 ◽  
Vol 14 (7) ◽  
pp. 3636-3640
Author(s):  
Xu Li ◽  
Mohammad R Farahani ◽  
Mehdi Rezaei ◽  
Muhammad K Siddiqui ◽  
Jia-Bao Liu ◽  
...  
Keyword(s):  
Polycyclic Aromatic Hydrocarbons ◽  
Aromatic Hydrocarbons ◽  
Wiener Index ◽  
Closed Formula ◽  
Cut Method ◽  
Polycyclic Aromatic

Ein einfaches graphentheoretisches Verfahren zur Abschatzung der Resonanz- und Grenzorbitalenergien alternierender polycyclisdier aromatisdier Kohlenwasserstoffe / A Simple Graph-theoretical Scheme for the Estimation of Resonance and Frontier Orbital Energies of Alternant Polycyclic Aromatic Hydrocarbons

1981 ◽  
Vol 36 (3) ◽  
pp. 276-279 ◽  
Author(s):  
K.-D. Gundermann ◽  
C. Lohberger ◽  
M. Zander
Keyword(s):  
Polycyclic Aromatic Hydrocarbons ◽  
Aromatic Hydrocarbons ◽  
Topological Index ◽  
Simple Graph ◽  
Frontier Orbital ◽  
Orbital Energies ◽  
Theoretical Scheme ◽  
Polycyclic Aromatic ◽  
Aromatic Systems ◽  
Condensed Systems

From the characteristic graphs of alternant polycyclic aromatic hydrocarbons (kata-annellated and peri-condensed systems) a topological index is derived, which can be calculated very easily even for highly complex aromatic systems and correlates satisfactorily with both the Dewar resonance and HMO frontier orbital energies. The graph-theoretical scheme provides a simple means for the rapid estimation of these data for unknown aromatic systems

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