scholarly journals Weighted Wiener Indices of Molecular Graphs with Application to Alkenes and Alkadienes

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 153
Author(s):  
Simon Brezovnik ◽  
Niko Tratnik ◽  
Petra Žigert Pleteršek
Keyword(s):  
Linear Regression Analysis ◽  
Chemical Properties ◽  
Wiener Index ◽  
Topological Indices ◽  
The Other ◽  
Multiple Bonds ◽  
Saturated Hydrocarbons ◽  
Simple Graphs ◽  
Boiling Points ◽  
Physico Chemical

There exist many topological indices that are calculated on saturated hydrocarbons since they can be easily modelled by simple graphs. On the other hand, it is more challenging to investigate topological indices for hydrocarbons with multiple bonds. The purpose of this paper is to introduce a simple model that gives good results for predicting physico-chemical properties of alkenes and alkadienes. In particular, we are interested in predicting boiling points of these molecules by using the well known Wiener index and its weighted versions. By performing the non-linear regression analysis we predict boiling points of alkenes and alkadienes.

scholarly journals Extremal Chemical Trees

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 .

Extremal Chemical Trees

2002 ◽  
Vol 57 (9-10) ◽  
pp. 49-52 ◽  
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.

Topological characterization of dendrimer, benzenoid, and nanocone

2018 ◽  
Vol 74 (1-2) ◽  
pp. 35-43
Author(s):  
Wei Gao ◽  
Muhammad Kamran Siddiqui ◽  
Najma Abdul Rehman ◽  
Mehwish Hussain Muhammad
Keyword(s):  
Chemical Properties ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Zagreb Index ◽  
Topological Characterization ◽  
Complex Molecules ◽  
Chemical Structures ◽  
Physico Chemical ◽  
Quantitative Structure Activity Relationships

Abstract Dendrimers are large and complex molecules with very well defined chemical structures. More importantly, dendrimers are highly branched organic macromolecules with successive layers or generations of branch units surrounding a central core. Topological indices are numbers associated with molecular graphs for the purpose of allowing quantitative structure-activity relationships. These topological indices correlate certain physico-chemical properties such as the boiling point, stability, strain energy, and others, of chemical compounds. In this article, we determine hyper-Zagreb index, first multiple Zagreb index, second multiple Zagreb index, and Zagreb polynomials for hetrofunctional dendrimers, triangular benzenoids, and nanocones.

scholarly journals On the Multiplicative Degree-Based Topological Indices of Silicon-Carbon Si2C3-I[p,q] and Si2C3-II[p,q]

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 320 ◽  
Author(s):  
Young Kwun ◽  
Abaid Virk ◽  
Waqas Nazeer ◽  
M. Rehman ◽  
Shin Kang
Keyword(s):  
Molecular Structure ◽  
Graph Theory ◽  
Molecular Graph ◽  
Chemical Properties ◽  
Topological Indices ◽  
Molecular Compound ◽  
Zagreb Indices ◽  
Silicon Carbon ◽  
Physico Chemical ◽  
Structure Research

The application of graph theory in chemical and molecular structure research has far exceeded people’s expectations, and it has recently grown exponentially. In the molecular graph, atoms are represented by vertices and bonds by edges. Topological indices help us to predict many physico-chemical properties of the concerned molecular compound. In this article, we compute Generalized first and multiplicative Zagreb indices, the multiplicative version of the atomic bond connectivity index, and the Generalized multiplicative Geometric Arithmetic index for silicon-carbon Si2C3−I[p,q] and Si2C3−II[p,q] second.

scholarly journals On the Multiplicative Degree-Based Topological Indices of Silicon-Carbon Si2C3-I[p,q] and Si2C3-II[p,q]

2018 ◽  
Author(s):  
Young Chel Kwun ◽  
Abaid ur Rehman Virk ◽  
Waqas Nazeer ◽  
Shin Min Kang
Keyword(s):  
Molecular Structure ◽  
Graph Theory ◽  
Molecular Graph ◽  
Chemical Properties ◽  
Topological Indices ◽  
Molecular Compound ◽  
Silicon Carbon ◽  
Physico Chemical ◽  
Structure Research

The application of graph theory in chemical and molecular structure research far exceeds people's expectations, and it has recently grown exponentially. In the molecular graph, atoms are represented by vertices and bonded by edges. Closed forms of multiplicative degree-based topological indices which are numerical parameters of the structure and determine physico-chemical properties of the concerned molecular compound. In this article, we compute and analyze many multiplicative degree-based topological indices of silicon-carbon Si2C3-I[p,q] and Si2C3-II[p,q].

scholarly journals Zagreb Polynomials and redefined Zagreb indices of nanostar dendrimers

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 31-40 ◽  
Author(s):  
Shin Min Kang ◽  
Muhammad Yousaf ◽  
Manzoor Ahmad Zahid ◽  
Muhammad Younas ◽  
Waqas Nazeer
Keyword(s):  
Boiling Point ◽  
Strain Energy ◽  
Chemical Properties ◽  
Topological Indices ◽  
Central Core ◽  
Zagreb Indices ◽  
Physico Chemical

Abstract Dendrimers are profoundly extended natural macromolecules with successive layers of branch units encompassing a central core. Topological indicess are numbers related with graph of a compound to allow quantitative structureactivity/property/lethality connections. These topological indices relate certain physico-chemical properties like stability, boiling point, strain energy and so forth of a compound. In this report, there have been computed redefined first, second and third Zagreb indices of Nanostar dendrimers. The authors also analyzed some Zagreb polynomials of understudy dendrimers.

scholarly journals Studies on Cyanex-272 Complexes of Mg (II), Ca (II) and Fe (III)

1970 ◽  
Vol 42 (4) ◽  
pp. 475-482 ◽  
Author(s):  
M Badrul Islam ◽  
M Zahurul Haque ◽  
N Shamsul Islam
Keyword(s):  
Key Words ◽  
Magnetic Measurements ◽  
Phosphinic Acid ◽  
Chemical Properties ◽  
Decomposition Temperature ◽  
Complex Compounds ◽  
The Other ◽  
Spectral Studies ◽  
Cyanex 272 ◽  
Physico Chemical

Certain complex compounds were synthesized by the interaction of Mg(II), Ca(II) and Fe(III) halides with the solvent extracting reagent, Cyanex-272 i.e. bis (2,4,4- trimethylpentyl) phosphinic acid as ligand. All the prepared complexes have been characterized on the basis of their molar masses, conductivity, magnetic measurements and infrared and electronic spectral studies. The other physico-chemical properties e.g. colour, decomposition temperature have also been ascertained. Key words: Chanex-272 Bangladesh J. Sci. Ind. Res. 42(4), 475-482, 2007

Wiener Indices and Molecular Surfaces

1995 ◽  
Vol 50 (7) ◽  
pp. 669-671 ◽  
Author(s):  
Ivan Gutmana ◽  
Tamás Körtvélyesi
Keyword(s):  
Volume Ratio ◽  
Wiener Index ◽  
Molecular Surface ◽  
Molecular Volume ◽  
Saturated Hydrocarbons ◽  
Molecular Surfaces ◽  
Physico Chemical ◽  
First Time

A correlation between the Wiener index (W) and the molecular surface of the respective alkane is established for the first time. This correlation is curvilinear and not particularly good. W is only weakly correlated to molecular volume of saturated hydrocarbons and does not reflect at all their surface-to-volume ratio. By this a long-existing controversy concerning the physico-chemical interpretation of W is resolved.

scholarly journals A new approach in topological descriptors usage. Iterated line graphs in the theoretical prediction of physico-chemical properties of saturated hydrocarbons

2019 ◽  
Keyword(s):  
Boiling Point ◽  
Molecular Graph ◽  
Chemical Properties ◽  
Topological Descriptors ◽  
Vaporization Enthalpy ◽  
Line Graphs ◽  
Regression Equations ◽  
Saturated Hydrocarbons ◽  
Program Complex ◽  
Physico Chemical

A new look on the problem of the molecular systems index description is presented. The capabilities of iterated line (edge) graphs in characterization of saturated hydrocarbons properties were investigated. It was demonstrated that single selected molecular (graph-theoretical (topological) or informational) descriptor calculated for the sequence of nested line graphs provides quite reliable progressive set of regression equations. Hence, the problem of descriptor set reduction is solved in the presented approach at list partially. Corresponding program complex (QUASAR) has been implemented with Python 3 program language. As the test example physico-chemical properties of octane isomers have been chosen. Among the properties under investigation there are boiling point, critical temperature, critical pressure, enthalpy of vaporization, enthalpy of formation, surface tension and viscosity. The corresponding rather simple linear regression equations which include one, two or three parameters correspondingly have been obtained. The predictive ability of the equations has been investigated using internal validation tests. The test by leave-one-out (LOO) validation and Y‑scrambling evaluate the obtained equations as adequate. For instance, for the regression model for boiling point the best equation characterizes by determination coefficients R2 = 0.943, with LOO procedure – Q2 = 0.918, while for the Y-scrambling test Q2y-scr<0.3 basically. It is shown that all the abovementioned molecular properties in iterated line graph approach can be effectively described by commonly used topological indices. Namely almost every randomly selected topological index can give adequate equation. Effectiveness is demonstrated on the example of Zagreb group indices. Also essential effectiveness and rather universal applicability of the so-called “forgotten” index (ZM3) was demonstrated.

scholarly journals Towards a Conceptual Understanding of Groundwater Ecology

2012 ◽  
Vol 1 (3) ◽  
pp. 493
Author(s):  
H.O Nwankwoala
Keyword(s):  
Conceptual Understanding ◽  
Chemical Properties ◽  
The Other ◽  
Ecological Communities ◽  
Groundwater Hydrology ◽  
Future Perspectives ◽  
Natural Ecosystems ◽  
Ecological Processes ◽  
Physico Chemical ◽  
Groundwater Ecology

In recent times, ecohydrology and hydroecology are making a mark on theenvironmental agenda, as evidenced by the proliferation of these terms in theacademic literature. There is an increasing recognition that groundwater is essentialto many ecological communities. Surface ecological processes (such asevapotranspiration) significantly impact hydrological responses and relatedhydrochemical function. Thus, the relation of groundwater hydrology to patternsand processes in ecology is a ‘two-way street’ where understanding the feedback ofone to the other serves as a powerful lens through which to evaluate and explainthe functioning of natural ecosystems. Influxes of groundwater to lakes, rivers, andwetlands can change whole-system physico-chemical properties such astemperature and salinity, while also providing more subtle influences onmicroenvironments and their ecological processes. The recognition of thesignificance and power of this tandem has not always been followed with effectiveinterdisciplinary science. The ecological, hydrological, and physico-chemical linksbetween groundwater, surface water and associated ecosystems are seldom fullyunderstood even though true characterization and wise management will require amultidisciplinary approach. This means biologists need to understand theimportance of magnitude and timing of groundwater flows for their system, whichrequires the skills of hydrogeologists to achieve. Hydrogeologists, in turn, mustunderstand how and why groundwater influences ecological processes so that theirexpertise is brought to bear at a scale commensurate to the ecological researchquestion. In this paper therefore, an overview of general concepts, research effortsand future perspectives are presented. More importantly, the paper asserts that it isnot simply the integration of hydrology and ecology that will determine the futureprospects for ecohydrology/hydroecology, but the way in which this integrativescience is conducted.

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