Department of Mathematics
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Item Reverse Degree Based Topological Indices of Chemical Graphs(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Muhammad Tayyab Younas; CIIT/FA19-RMT-064/LHR; Dr. Muhammad Kamran Siddiqui; LHR TP 7428Graph theory is playing a key role in applied and pure mathematics. The scope of graph theory is expanding day by day. In this thesis, we have evaluated some reverse degree based topological indices, namely, the reverse general Randic index for ∝= 1, −1, 1 2 , − 1 2 , the reverse atom bond connectivity index, the reverse geometric arithmetic index, the reverse first and second Zagreb indices, the reverse first and second Zagreb co-indices, the reverse forgotten index, the reverse hyper Zagreb index, the reverse Balaban index, the reverse first and second multiple Zagreb indices, the reverse redefined first, second and third Zagreb indices for some chemical and lattices graphs like as Remdesivir, transition metal tetra cyano benzene organic network (𝑇𝑀 − 𝑇𝐶𝑁𝐵),metal organic superlattice and trans-Pd-(𝑁𝐻2)S lattice. My thesis comprising of five chapters. In the first chapter we will define some fundamental definitions. In the 2nd chapter, we will find reverse degree based topological indices for Remdesivir and transition metal tetra cyano benzene organic network (𝑇𝑀 − 𝑇𝐶𝑁𝐵). In the 3rd chapter, we will find reverse degree based topological indices for metal organic superlattice and trans-Pd-(𝑁𝐻2)S lattice. In the 4th chapter, we will present the conclusion of our thesis. In the 5th chapter, we will present the references of our thesis.Item Resolving Topological Index Of Graphs Associated(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Ali Bahadar; FA19-RMT-109; Dr. Kashif Ali; LHR TP 7394In this thesis, we study a well-known concept of graph theory, called resolvability, in con- text of two types of graphs ( commuting and non-commuting) associated to two algebraic structures (dihedral and semi-dihedral groups). By analyzing the resolving share and the average resolving share of each vertex, we compute the resolving topological index of each graph.Item Topological Indices of Fuzzy Graphs(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Arslan Kaleem; CIIT/FA19-RMT-108/LHR; Dr. Imran Ahmed; LHR TP 7405In this thesis, We study the topological indices of fuzzy graphs. A topological index is a numerical number for a structural graph of a molecule. It plays an important role in mathe- matical chemistry. We intend to study topological indices of graphs and fuzzy graphs. We establish the relation between first Gourava index and first Gourava co-index. We define some new topological indices of fuzzy graphs. Then we determine the relation between first Zagreb index(respectively second Zagreb index) of fuzzy graph and first Zabreb in- dex(respectively second Zagreb index) of its complete fuzzy graph.Item Topological Indices of Boron Nano Tubes and Some Chemical Graphs(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) HAFIZ MUHAMMAD ASIF MEHMOOD; CIIT/FA19-RMT-114/LHR; Dr. Hani Shaker; LHR TP 7438The goal of this research study is to discuss some degree based topological descriptors of molecular graphs of (Boron Nano Tubes) by the assistance of fundamental ideas of graph theory. Using different terminologies we will calculate degree-based topological indices like “Gourava Indices”, “Shigehalli and Kanabur Indices”, “Sanskruti Index” of Boron Nano Tubes and also find some multiplicative version of above discussed topological indices of different molecular graphs.Item Topological Indices on Line Graph of Multi Web and Multi Jahangir Graph(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Awais Amanat; CIIT/FA19-RMT-082/LHR; Dr. Imran Zulfiqar Cheema; LHR TP 7414A topological index is a numeric measure from the molecular graph. Usage of topological indices in chemistry is remarkable. In a structure related graph, a real number that always remains constant is called a topological index. A great number of topological indices have been presented till date, several of them are being applied in different industries as means like pharmaceutical industry modal chemical industry etc. In this thesis, we will calculate the degree based topological indices so-called Randic index, atom bond connectivity (ABC) index, geometric arithmetic (GA) index, first and second Zagreb, third Zagreb, hyper Zagreb, Harmonic index, F-index, Redefined first, second and third Zagreb indices, Sum connectivity index for line graph of multi- Web graph (𝑊𝑛,𝑚) (Tn × Cm) where m ≥ 5 and n ≥ 2 and as well as line graph of multi- Jahangir graph (𝐽𝑛,𝑚) where n ≥ 4 m ≥ 3. We will also compute degree sum based topological indices ABC₄ index known as the fourth version of atom bond connectivity (ABC) index and GA₅ index which is the fifth class of geometric arithmetic (GA) index for these graphsItem Statistical Analysis of some Chemical Network with respect to Several Topological Indices(Library Information Services COMSATS University Lahore Campus, 2024-03-14) Fakhra Younas; FA22-RMT-036; Prof. Dr. Muhammad Hussain; LHR TP 9357Statistical Analysis of some Chemical Network with respect to Several Topological IndicesItem M-Polynomias and Degree Base Topological Indices of Strontium Structure(Library Information Services COMSATS University Lahore Campus, 2023-03-13) Maryam Javed; SP22-RMT-018; Dr. M. Faisal Nadeem; LHR TP 8725M-Polynomias and Degree Base Topological Indices of Strontium StructureItem Eccentricity based Topological Indices on Associated Line Graphs of Different Chemical Networks(Library Information Services COMSATS University Lahore Campus, 2023-03-13) Jamila Faryal; SP22-RMT-002; Prof. Dr. Muhammad Hussain; LHR TP 8711Graph theory acts as an essential tool in various fields and applications because of its versatility in modeling and solving problems involving relationships and connections. In this thesis, our aim is to compute the eccentricity based topological indices like to tal eccentricity, Zagreb indices, average eccentricity, Geometric Arithmetic index GA, atom-bond connectivity ABC index for the line graphs of first type of Hex-Derived Networks HDN1(s) as well as some other chemical structures. Furthermore, the basic topologies of these networks are also derived. We obtained their respective indices based on the categorization of the chemical graphs. These newly obtained indices give insight into the chemical and physical properties of molecules. This analysis will assist researchers engaged in the field of network sciences by clarifying the structure of the aforementioned networks. Moreover, the results presented in this thesis might offer ad vantages in predicting supplementary chemical, physical and structural characteristics of the molecular graphs being studied.Item DEGREE BASE TOPOLOGICAL INDICES OF SOME FAMILIES OF GRAPHS(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2016) Mahrukh; SP15-RMT-009; LHR TP 6828; Dr. Kashif AliAtopological index is a numerical value associated with chemical constitution for cor relation of chemical structure with various physical properties, chemical reactivity or biological activity. In this thesis, we will discuss the different degree based topological indices i.e. Randic index, Zagreb index, Atom-bond connectivity index, Geometric arithmetic index, Augmented Zagreb index, Harmonic index, Sum-connectivity index for benzene BCZ, Benzene BTA diamond like graph, line graph of ladder and line graph of nanostar dendrimers. We will also compute ABC4 and GA5 for benzene BCZ, Benzene BTA diamond like graphItem Exploring Topological Indices for Magnesium Nitrogen via Curve Fitting Model(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Nida Ahsan (FA23-RMT-046); Dr. Muhammad Kamran Siddiqui; LHR TP 9789The use of graph theory in many fields of study has increased significantly, especially in the field of chemical graph theory. Many scholars have been able to explore a range of new directions in the last few years. A chemical graph is a named graph in which the atoms of a compound are represented at the vertices, and the edges represent chemical bonds between atoms. Determining various physical and chemical properties of the molecular structures under study requires an examination of topological indices. Firstly, we focused on degree-based topological indices, namely the Randic´ index, atom bond connectivity in- dex, geometric arithmetic index, the first and the second Zagreb indices and co-indices, the first and the second multiple Zagreb indices and co-indices, hyper Zagreb index, for- gotten index, augmented Zagreb index, Balaban index, redefined Zagreb type indices, of Magnesium Nitrogen MgN4. Afterward, we found the physical measures like the heat of formation of Magnesium Nitrogen MgN4. Then, we fitted curves between different indices and the corresponding heat of formation. 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. Fur- ther, we gave graphical representations of these indices. These mathematical frameworks might provide a way to study the thermo dynamical properties of the chemical structure Magnesium Nitrogen MgN4