Electron Energy Studying of Molecular Structures via Forgotten Topological Index Computation

It is found from the earlier studies that the structure-dependency of totalπ-electron energyEπheavily relies on the sum of squares of the vertex degrees of the molecular graph. Hence, it provides a measure of the branching of the carbon-atom skeleton. In recent years, the sum of squares of the vertex degrees of the molecular graph has been defined as forgotten topological index which reflects the structure-dependency of totalπ-electron energyEπand measures the physical-chemical properties of molecular structures. In this paper, in order to research the structure-dependency of totalπ-electron energyEπ, we present the forgotten topological index of some important molecular structures from mathematical standpoint. The formulations we obtained here use the approach of edge set dividing, and the conclusions can be applied in physics, chemical, material, and pharmaceutical engineering.

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Physical-chemical properties studying of molecular structures via topological index calculating

Open Physics ◽

10.1515/phys-2017-0029 ◽

2017 ◽

Vol 15 (1) ◽

pp. 261-269

Author(s):

Jianzhang Wu ◽

Mohammad Reza Farahani ◽

Xiao Yu ◽

Wei Gao

Keyword(s):

Topological Index ◽

Chemical Properties ◽

Molecular Structures ◽

Connectivity Index ◽

Chemical Characteristics ◽

Eccentric Connectivity Index ◽

Distance Computation ◽

Physical Chemical ◽

Mathematical Derivation ◽

Mathematical Standpoint

AbstractIt’s revealed from the earlier researches that many physical-chemical properties depend heavily on the structure of corresponding moleculars. This fact provides us an approach to measure the physical-chemical characteristics of substances and materials. In our article, we report the eccentricity related indices of certain important molecular structures from mathematical standpoint. The eccentricity version indices of nanostar dendrimers are determined and the reverse eccentric connectivity index for V-phenylenic nanotorus is discussed. The conclusions we obtained mainly use the trick of distance computation and mathematical derivation, and the results can be applied in physics engineering.

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Choosing the exponent in the definition of the connectivity index

Journal of the Serbian Chemical Society ◽

10.2298/jsc0109605g ◽

2001 ◽

Vol 66 (9) ◽

pp. 605-611 ◽

Cited By ~ 13

Author(s):

Ivan Gutman ◽

Mirko Lepovic

Keyword(s):

Carbon Atom ◽

Topological Index ◽

Organic Molecules ◽

Molecular Graph ◽

Chemical Properties ◽

Connectivity Index ◽

Physico Chemical ◽

Definition Of ◽

Molecular Branching ◽

Suitable Measure

Let ?v denote the degree of the vertex v of a molecular graph G. Then the connectivity index of G is defined as C (?) = G (?,C) = ? (?u?v)?, where the summation goes over all pairs of adjacent vertices. The exponent ? is usually chosen to be equal to -1/2, but other options were considered as well, especially ?=-1. We show that whereas C(-1/2) is a suitable measure of branching of the carbon-atom skeleton of organic molecules, and thus applicable as a topological index for modeling physico-chemical properties of the respective compounds, this is not the case with C(-1). The value of ? is established, beyond which C(?) fails to correctly reflect molecular branching.

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Extremal Chemical Trees

Zeitschrift für Naturforschung A ◽

10.1515/zna-2002-1-206 ◽

2002 ◽

Vol 57 (1-2) ◽

pp. 49-51

Author(s):

Miranca Fischermann ◽

Ivan Gutman ◽

Arne Hoffmann ◽

Dieter Rautenbach ◽

Dušica Vidovića ◽

...

Keyword(s):

Carbon Atom ◽

Molecular Graph ◽

Chemical Properties ◽

Wiener Index ◽

Graph Representation ◽

Hosoya Index ◽

Saturated Hydrocarbons ◽

Physico Chemical ◽

Graph Energy ◽

Chemical Trees

A variety of molecular-graph-based structure-descriptors were proposed, in particular the Wiener index W. the largest graph eigenvalue λ1, the connectivity index X, the graph energy E and the Hosoya index Z, capable of measuring the branching of the carbon-atom skeleton of organic compounds, and therefore suitable for describing several of their physico-chemical properties. We now determine the structure of the chemical trees (= the graph representation of acyclic saturated hydrocarbons) that are extremal with respect to W , λ1, E, and Z. whereas the analogous problem for X was solved earlier. Among chemical trees with 5. 6, 7, and 3k + 2 vertices, k = 2,3,..., one and the same tree has maximum λ1 and minimum W, E, Z. Among chemical trees with 3k and 3k +1 vertices, k = 3,4...., one tree has minimum 11 and maximum λ1 and another minimum E and Z .

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New Results on the Forgotten Topological Index and Coindex

Journal of Mathematics ◽

10.1155/2021/8700736 ◽

2021 ◽

Vol 2021 ◽

pp. 1-11

Author(s):

Akbar Jahanbani ◽

Maryam Atapour ◽

Rana Khoeilar

Keyword(s):

Electron Energy ◽

Connected Graph ◽

Topological Index ◽

Nonadjacent Vertex ◽

Zagreb Indices ◽

Vertex Degrees ◽

Simple Connected Graph

The ℱ -coindex (forgotten topological coindex) for a simple connected graph G is defined as the sum of the terms ζ G 2 y + ζ G 2 x over all nonadjacent vertex pairs x , y of G , where ζ G y and ζ G x are the degrees of the vertices y and x in G , respectively. The ℱ -index of a graph is defined as the sum of cubes of the vertex degrees of the graph. This was introduced in 1972 in the same paper where the first and second Zagreb indices were introduced to study the structure dependency of total π -electron energy. Therefore, considering the importance of the ℱ -index and ℱ -coindex, in this paper, we study these indices, and we present new bounds for the ℱ -index and ℱ -coindex.

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Topological study of the para-line graphs of certain pentacene via topological indices

Open Chemistry ◽

10.1515/chem-2018-0126 ◽

2018 ◽

Vol 16 (1) ◽

pp. 1200-1206 ◽

Cited By ~ 1

Author(s):

Zeeshan Saleem Mufti ◽

Muhammad Faisal Nadeem ◽

Wei Gao ◽

Zaheer Ahmad

Keyword(s):

Molecular Structure ◽

Real Number ◽

Chemical Structure ◽

Topological Index ◽

Line Graph ◽

Chemical Properties ◽

Topological Indices ◽

Molecular Structures ◽

Line Graphs ◽

Graph Invariant

AbstractA topological index is a map from molecular structure to a real number. It is a graph invariant and also used to describe the physio-chemical properties of the molecular structures of certain compounds. In this paper, we have investigated a chemical structure of pentacene. Our paper reflects the work on the following indices:Rα, Mα, χα, ABC, GA, ABC4, GA5, PM1, PM2, M1(G, p)and M1(G, p) of the para-line graph of linear [n]-pentacene and multiple pentacene.

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

Current Organic Synthesis ◽

10.2174/1570179418666210309145043 ◽

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.

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Extremal Chemical Trees

Zeitschrift für Naturforschung A ◽

10.1515/zna-2002-9-1006 ◽

2002 ◽

Vol 57 (9-10) ◽

pp. 49-52 ◽

Cited By ~ 22

Author(s):

Miranca Fischermann ◽

Ivan Gutmana ◽

Arne Hoffmann ◽

Dieter Rautenbach ◽

Dušica Vidović ◽

...

Keyword(s):

Carbon Atom ◽

Molecular Graph ◽

Chemical Properties ◽

Wiener Index ◽

Graph Representation ◽

Hosoya Index ◽

Saturated Hydrocarbons ◽

Physico Chemical ◽

Graph Energy ◽

Chemical Trees

Avariety of molecular-graph-based structure-descriptors were proposed, in particular the Wiener index W, the largest graph eigenvalue λ1, the connectivity index χ, the graph energy E and the Hosoya index Z, capable of measuring the branching of the carbon-atom skeleton of organic compounds, and therefore suitable for describing several of their physico-chemical properties. We now determine the structure of the chemical trees (= the graph representation of acyclic saturated hydrocarbons) that are extremal with respect to W, λ1, E, and Z, whereas the analogous problem for χ was solved earlier. Among chemical trees with 5, 6, 7, and 3k + 2 vertices, k = 2, 3,..., one and the same tree has maximum λ1 and minimum W, E, Z. Among chemical trees with 3k and 3k + 1 vertices, k = 3, 4..., one tree has minimum W and maximum λ1 and another minimum E and Z.

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VDB Entropy Measures and Irregularity-Based Indices for the Rectangular Kekulene System

Journal of Mathematics ◽

10.1155/2021/7404529 ◽

2021 ◽

Vol 2021 ◽

pp. 1-15

Author(s):

Weidong Zhao ◽

K. Julietraja ◽

P. Venugopal ◽

Xiujun Zhang

Keyword(s):

Coal Gasification ◽

Molecular Graph ◽

Chemical Properties ◽

Mathematical Expression ◽

Cost Effective ◽

Molecular Structures ◽

Specific Chemical ◽

Chemical Structures ◽

Broad Array ◽

Polycyclic Aromatic

Theoretical chemists are fascinated by polycyclic aromatic hydrocarbons (PAHs) because of their unique electromagnetic and other significant properties, such as superaromaticity. The study of PAHs has been steadily increasing because of their wide-ranging applications in several fields, like steel manufacturing, shale oil extraction, coal gasification, production of coke, tar distillation, and nanosciences. Topological indices (TIs) are numerical quantities that give a mathematical expression for the chemical structures. They are useful and cost-effective tools for predicting the properties of chemical compounds theoretically. Entropic network measures are a type of TIs with a broad array of applications, involving quantitative characterization of molecular structures and the investigation of some specific chemical properties of molecular graphs. Irregularity indices are numerical parameters that quantify the irregularity of a molecular graph and are used to predict some of the chemical properties, including boiling points, resistance, enthalpy of vaporization, entropy, melting points, and toxicity. This study aims to determine analytical expressions for the VDB entropy and irregularity-based indices in the rectangular Kekulene system.

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F-Index of some graph operations

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830916500257 ◽

2016 ◽

Vol 08 (02) ◽

pp. 1650025 ◽

Cited By ~ 18

Author(s):

Nilanjan De ◽

Sk. Md. Abu Nayeem ◽

Anita Pal

Keyword(s):

Electron Energy ◽

Topological Index ◽

Zagreb Index ◽

Zagreb Indices ◽

Molecular Graphs ◽

Basic Properties ◽

Graph Operations ◽

Physico Chemical ◽

Vertex Degrees

The F-index of a graph is defined as the sum of cubes of the vertex degrees of the graph. This was introduced in 1972, in the same paper where the first and second Zagreb indices were introduced to study the structure-dependency of total [Formula: see text]-electron energy. But this topological index was not further studied till then. Very recently, Furtula and Gutman [A forgotten topological index,J. Math. Chem. 53(4) (2015) 1184–1190.] reinvestigated the index and named it “forgotten topological index” or “F-index”. In that paper, they present some basic properties of this index and showed that this index can enhance the physico-chemical applicability of Zagreb index. Here, we study the behavior of this index under several graph operations and apply our results to find the F-index of different chemically interesting molecular graphs and nanostructures.

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