Browsing by Author "Mazhar Hussain"

Now showing 1 - 3 of 3

Describing Topology of Chemical Compounds Using Graphical Descriptors
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Mazhar Hussain; CIIT/SP20-RMT-004/LHR; Dr. Sana Javed; LHR TP 7623
In terms of graph theory, a molecular graph or chemical graph is a representation of the structural formula of a chemical compound. A chemical graph is a labeled graph in which the vertices represent the atoms of a compound and the edges represent chemical bonds between two atoms. In this thesis, we computed various connectivity indices based on degrees of vertices of chemical graph of Iron(III) Oxide (𝐹𝑒2𝑂3) and Titanium Dioxide (𝑇𝑖𝑂2) including general Randic, ABC, GA and Zagreb indices etc. Afterwards, we found the physical measures like entropy and heat of formation of Iron(III) Oxide (𝐹𝑒2𝑂3) and Titanium Dioxide (𝑇𝑖𝑂2). Then, we fitted curves between different indices and the thermodynamical properties namely heat of formation and entropy. Curve fitting was done in MATLAB through different methods based on linearity and non-linearity. The performance of the method was tested using mean squared error (MSE), the sum of squared errors (SSE) or R2. Further, we gave graphical representations of these indices. These mathematical frameworks might provide a way to study the thermodynamical properties of the chemical structure Iron(III) Oxide (𝐹𝑒2𝑂3) and Titanium Dioxide (𝑇𝑖𝑂2) at intense level which will assist to comprehend the relationship between system dimension and these measures. This thesis is divided into five chapters. Chapter 1 contains basic definitions, notions and terminologies related to this thesis. Chapter 2 provides a review of literature about our work. The main results are given in chapter 3. Chapter 4 contains a brief discussion about the work while chapter 5 consist of the references used in this thesis.
On Group Labeling of Antiprism Graphs
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Mazhar Hussain; CIIT/SP20-RMT-038/LHR; Dr. Hani Shaker; LHR TP 7640
Assume a graph G with n vertices and Λ be any abelian group having n elements. Group distance magic labeling of G is a bijective map f: V → Λsuch that ∃μ∈Λ for that ∑ ∈ ( ) ( ) = ∀ v ∈ V, where are the vertices adjacent to v. In this thesis , we find the × × × , × × × , × × × , × × × , × × × , × × × , group distance magic labeling for antiprism graph !
Study of Thermal Stability and Thermodynamic Geometries of Well-Known Black Holes through Entropy Corrections
(Library Information Services, CUI Lahorez v, 2023) Mazhar Hussain; FA20-RMT-017; Dr. Abdul Jawad
In this thesis, we investigate the thermal stability and thermodynamic geometries of non-rotating/rotating charged black holes. For these black holes, we apply Barrow and power-law entropy to determine the physical quantities such as mass and temperature of the system and ¯nd their sta- bility through ¯rst and second phase transitions of the heat capacity. We analyze the e®ects of scalar charge Q and hair parameter ¸ on black holes properties by taking both positive and negative values of these parame- ters. It is noted that heat capacity provide the stable, unstable regions and phase transition points for both black holes. To investigate the thermody- namic geometry of these black holes, various techniques such as Ruppeiner, Weinhold, Quevedo and HPEM metrics are considered. It is observed that Weinhold, Quevedo and HPEM give attrative/repulsive behavior of parti- cles in stable/unstable regions of black holes.