Computation of three topological indices on some molecular graphs and families of nanostar dendrimers
Chemical graph theory is a branch of mathematical chemistry which applies graph theory in mathematical modeling of chemical phenomena. One of the most active fields of research in chemical graph theory is the study of topological indices that can be used for describing and predicting physicochemical...
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myupmir.7717820200305T01:57:16Z Computation of three topological indices on some molecular graphs and families of nanostar dendrimers 201806 Haoer, Raad Sehen Chemical graph theory is a branch of mathematical chemistry which applies graph theory in mathematical modeling of chemical phenomena. One of the most active fields of research in chemical graph theory is the study of topological indices that can be used for describing and predicting physicochemical and pharmacological properties of organic compounds. A topological index is a single unique number characteristic of the molecular graph and is mathematically known as the graph invariant. Eccentric connectivity Index, Zagrebeccentricity indices and Wiener index are three of the most popular topological indices and used in wide spectrum of applications in chemical graph theory. Motivated by the works done on characterization of mathematical properties for some nanostructures (dendrimers, nanotubes, nanotori, fullerenes etc.), we continue to investigate and obtain novelty formulas of the eccentric connectivity index for unicyclic chemical graph, chemical trees and some families of nanostar dendrimers. Also, we consider novelty formulas of the Zagrebeccentricity indices for some families of nanostar dendrimers. Finally, novelty formulas for Wiener index of a new class of nanostar dendrimers are considered and new formulas associated with it are determined. In this thesis, we study and analyses the molecular structures and structural properties of chemical compounds with the objective to represent them graphically and construct new classes of graphs. We use mathematical methods of mathematical induction and mathematical logic to arrive at our theorems. In particular, the Eccentric Connectivity Indices ξ (G) are obtained for certain special graphs constructed by joining some special graphs to path graph. Through those graphs constructed are found ξ (G) for graphs associated with some of molecular graphs such as chemical trees, chemical unicyclic graphs and some infinite families of nanostar dendrimers. Also, the Zagrebeccentricity indices Z(G) are found for some families of chemical trees, chemical unicyclic graphs and some infinite families of nanostar dendrimers. Finally, novel formulas for Wiener index of some dendrimers such as Polyphenelene dendrimers are established. Based on these investigations and graphical analysis novel formulas for the topological indices of these chemical compounds and nanotechnology are then obtained. Chemistry  Mathematics Graph theory  Case studies Algebraic topology 201806 Thesis http://psasir.upm.edu.my/id/eprint/77178/ http://psasir.upm.edu.my/id/eprint/77178/1/IPM%202018%209%20%20IR.pdf text en public doctoral Universiti Putra Malaysia Chemistry  Mathematics Graph theory  Case studies Algebraic topology Md. Said, Mohamad Rushdan 
institution 
Universiti Putra Malaysia 
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PSAS Institutional Repository 
language 
English 
advisor 
Md. Said, Mohamad Rushdan 
topic 
Chemistry  Mathematics Graph theory  Case studies Algebraic topology 
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Chemistry  Mathematics Graph theory  Case studies Algebraic topology Haoer, Raad Sehen Computation of three topological indices on some molecular graphs and families of nanostar dendrimers 
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Chemical graph theory is a branch of mathematical chemistry which applies graph theory in mathematical modeling of chemical phenomena. One of the most active fields of research in chemical graph theory is the study of topological indices that can be used for describing and predicting physicochemical and pharmacological properties of organic compounds.
A topological index is a single unique number characteristic of the molecular graph and is mathematically known as the graph invariant. Eccentric connectivity Index, Zagrebeccentricity indices and Wiener index are three of the most popular topological indices and used in wide spectrum of applications in chemical graph theory.
Motivated by the works done on characterization of mathematical properties for some nanostructures (dendrimers, nanotubes, nanotori, fullerenes etc.), we continue to investigate and obtain novelty formulas of the eccentric connectivity index for unicyclic chemical graph, chemical trees and some families of nanostar dendrimers. Also, we consider novelty formulas of the Zagrebeccentricity indices for some families of nanostar dendrimers. Finally, novelty formulas for Wiener index of a new class of nanostar dendrimers are considered and new formulas associated with it are determined.
In this thesis, we study and analyses the molecular structures and structural properties of chemical compounds with the objective to represent them graphically and construct new classes of graphs. We use mathematical methods of mathematical induction and mathematical logic to arrive at our theorems. In particular, the Eccentric Connectivity Indices ξ (G) are obtained for certain special graphs constructed by joining some special graphs to path graph. Through those graphs constructed are found ξ (G) for graphs associated with some of molecular graphs such as chemical trees, chemical unicyclic graphs and some infinite families of nanostar dendrimers. Also, the Zagrebeccentricity indices Z(G) are found for some families of chemical trees, chemical unicyclic graphs and some infinite families of nanostar dendrimers. Finally, novel formulas for Wiener index of some dendrimers such as Polyphenelene dendrimers are established. Based on these investigations and graphical analysis novel formulas for the topological indices of these chemical compounds and nanotechnology are then obtained. 
format 
Thesis 
qualification_level 
Doctorate 
author 
Haoer, Raad Sehen 
author_facet 
Haoer, Raad Sehen 
author_sort 
Haoer, Raad Sehen 
title 
Computation of three topological indices on some molecular graphs and families of nanostar dendrimers 
title_short 
Computation of three topological indices on some molecular graphs and families of nanostar dendrimers 
title_full 
Computation of three topological indices on some molecular graphs and families of nanostar dendrimers 
title_fullStr 
Computation of three topological indices on some molecular graphs and families of nanostar dendrimers 
title_full_unstemmed 
Computation of three topological indices on some molecular graphs and families of nanostar dendrimers 
title_sort 
computation of three topological indices on some molecular graphs and families of nanostar dendrimers 
granting_institution 
Universiti Putra Malaysia 
publishDate 
2018 
url 
http://psasir.upm.edu.my/id/eprint/77178/1/IPM%202018%209%20%20IR.pdf 
_version_ 
1747813207221731328 