M.Phil / MS
Permanent URI for this collectionhttps://repository.cuilahore.edu.pk/handle/123456789/52
This collection archives the complete set of theses produced by students of the COMSATS University Islamabad, Lahore Campus.
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Item On Topological Aspects of Molecular Graph of Copper Sulfide(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Maryam Shahid; CIIT/SP24-RMT-011/LHR; Dr. Muhammad Kamran Siddiqui; LHR TP 10073The use of graph theory to 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 Randic index, atom bond connectivity index, 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, forgotten index, augmented Zagreb index, Balaban index, redefined Zagreb type indices, of Copper Sulfide Network CuS.Item Degree Based Topological Co-Indices of Chemical Graphs(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Nazir Hussain; CIIT/SP20-RMT-021/LHR; Dr. Muhammad Kamran Siddiqui; LHR TP 7631Graph 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 degree based topological co-indices, namely, the general Randic co-index for ∝= 1, −1, 1 2 , − 1 2 , the atom bond connectivity co- index, the geometric arithmetic co-index, the first and second Zagreb co-indices, the first and second Zagreb co-indices, the forgotten co-index, the hyper Zagreb co-index, the Balaban co-index, the first and second multiple Zagreb co-indices, the redefined first, second and third Zagreb co-indices for some chemical and lattices graphs like as line graph of Metal Organic Networks, Triangular Benzenoids Gn ⱯϵN, Zigzag edge cornoid fused with starphene zcs(k,l,m), Hony comb network (Hcn), Hydro chloroquine HCQ Conjugated Hydroxyethyl. My thesis comprising of eight chapters. In the first chapter we will define some fundamental definitions. In the 2nd chapter, we will find degree based topological Co- indices for line graph of Metal Organic Networks. In the 3rd chapter, we will find degree based topological Co- indices for Triangular Benzenoids Gn ⱯϵN. In the 4th chapter, we will find degree based topological Co- indices for Zigzag edge cornoid fused with starphene zcs(k,l,m). In the 5th chapter, we will find degree based topological Co- indices for Hony comb network (Hcn). In the 6th chapter, we will find degree based topological Co- indices for Hydro chloroquine HCQ Conjugated Hydroxyethyl. In the 7th chapter, we will present the conclusion of our thesis. In the last, we will present the references of our thesisItem Reverse Degree Based Topological Indices of Graph Products(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Inzimam Sajid; CIIT/SP20-RMT-035/LHR; Dr. Muhammad Kamran Siddiqui; LHR TP 7638Graph 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 𝛼 = 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 first and second multiple Zagreb indices, the reverse redefined first, second and third Zagreb indices for some reverse degree based topological indices for line graphs, Reverse Indices of various Products of graph. My thesis comprising of six chapters. In the first chapter we will define some fundamental definitions. In the 2nd chapter, we will find reverse degree based topological indices for various products of graphs. In the 3rd chapter, we will find reverse degree based topological indices for 𝐿(𝑀𝑂𝑁1(𝜒)). In the 4th chapter, reverse degree based topological indices for 𝐿(𝑀𝑂𝑁2(𝜒)). In the 5th chapter, we will present the conclusion of our thesis. In the 6th chapter, we will present the references of our thesis.Item Computing Degree Based Topological Indices of Calcium Hydroxide(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2022) Hammad Ali; CIIT/FA20-RMT-036LHR; Dr. Muhammad Kamran Siddiqui; LHR TP 7938‘Graph 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 computed some topological indices, Co-indices and reverse degree- based indices such as ffirst‘ and ‘second Zagreb‘co-index, first and‘second multiple ‘Zagreb co-index‘forgotton‘topological co-index, atom bond‘connectivity co- index,‘geometric arithmetic co-index , Balaban index and general‘Randic index ‘for‘∝ = 1, −1, 1 2 , − 1 2 ‘for Calcium Hydroxide. My thesis comprising of five chapters. In the first chapter, we will define some basic definitions. In the 2nd chapter, we will find topological indices of Calcium Hydroxide structure. In the 3rd chapter, we will find topological Co-Indices of Calcium Hydroxide structure. In the 4th chapter, we will find reverse degree based topological indices of Calcium Hydroxide structure. In the 5th chapter, we will present the conclusion of our thesis.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 On Some Regular Properties of Fuzzy Graph(Library Information Services COMSATS University Islamabad Lahore Campus, 2021) Mohsan Majeed; FA19-RMT-027; LHR TP 7388; Dr. Muhammad Kamran SiddiquiGraph 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 study the definition of fuzzy graph, complete fuzzy graph, strong fuzzy graph, regular fuzzy graph, totally regular fuzzy graph with illustrative example and properties of regular and totally regular fuzzy graph. We discuss the concept of uniform vertex and uniform edge fuzzy graph with examples also we check the results related to uniform vertex and uniform edge fuzzy graph. We see that the concept of uniform vertex and uniform edge fuzzy graph is useful in the study of regular and totally regular fuzzy graph. We also see the definition of complement of fuzzy graph and properties of self-complement fuzzy graph and we study some other operations on fuzzy graph such that union, join, composition, direct product, semi strong product and strong product. We read the notion of balanced fuzzy graph. At last we see the fuzzy soft graph, complete fuzzy soft graph, regular fuzzy soft graph, totally regular fuzzy soft graph with examples and some of their important properties. My thesis comprising of seven chapters. In the first chapter we will define of fuzzy graph regular fuzzy graph and totally regular fuzzy graph. In the 2th chapter, we will define uniform vertex fuzzy graph and uniform edge fuzzy graph. In the 3th chapter, we will discuss complement of fuzzy graph. We will check union and join of two fuzzy graphs. In the 4th chapter, we will discuss three more operations on fuzzy graph. In the 5th chapter, we will see the concept of the fuzzy soft graph and various types of fuzzy soft graph with examples. In the 6th chapter, we will present the conclusion of our thesis. In the 7th chapter, we will present the references of our thesis.Item Degree Based Topological Indices of Some Chemical Graphs(Library Information Services COMSATS University Islamabad Lahore Campus, 2021) Zafar Iqbal; FA19-RMT-037; LHR TP 7434; Dr. Muhammad Kamran SiddiquiGraph 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 computed some topological indices like as First and Second zagreb index, First and Second zagreb co-index, First and Second multiplicative zagreb index, Forgotten topological index, Hyper zagreb index, Atom bond connectivity index, Geometric arithmetic index, augmented zagreb index, Balaban index, general Randic index for ∝= 1, −1, 1 2 , − 1 2 and Redefined first, second and third zagreb index for some chemical graphs like as Hydroxy chloroquine, Chloroquine, H-Naphtalenic Nanosheet and Dexamethasone. My thesis comprising of four chapters. In the first chapter we will define some fundamental definitions and we will see the literature review. In the 2nd chapter, we will find indices for the chemical graph of Hydroxy chloroquine and Chloroquine and then we will draw the numerically and graphically comparison of different indices. In the 3rd chapter, we will find indices for the chemical graph of H-Naphtalenic nanosheet and Dexamethasone and then we will draw the numerically and graphically comparison of different indices. In the 4th chapter, we will present the conclusion of our thesis. At the last we will represent the reference of our thesis.Item Degree Based Topological Co-Indices of Graphs(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) Muhammad Nasir; SP19-RMT-032; LHR TP 6481; Dr. Muhammad Kamran SiddiquiGraph 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 computed some topological coindices like as First and Second zagreb co-index, First and Second multiplicative zagreb coindex, Forgotton topological coindex, Atom bond connectivity coindex, Geometric arithmetic coindex and general Randic coindex for ∝= 1,−1, ଵ ଶ ,−ଵ ଶ for some chemical and networking graphs like as David derived network; ??(2), Dominating david derived network; ???(2), Regular Triangular Silicate network of dimension n; ????(?), Triangular chain cactus; ??, Oraganosilicon dendrimer ?[?]; ? ≥ 1; 2, Para chain square cactus; ?? ,Ortho chain square cactus; ??, Tetrathiafulvalene dendrimers; ??2[?]. My thesis comprising of four chapters. In the first chapter we will define some fundamental definitions. In the 2nd chapter, we will find Co-indices for David derived network, dominating David derived network, Regular triangular silicate network of dimension ? and Oraganosilicon dendrimer ?[?] graphs. In the 3rd chapter, we will find Triangular chain cactus, Para chain square cactus, Ortho chain square cactus, Tetrathiafulvalene dendrimers. In the 4th chapter, we will present the conclusion of our thesis. In the last, we will present the refrences of our thesis.Item On VE and EV Degree Based Topological Index of Graphs(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) Aimen Wali; SP19-RMT-009; LHR TP 6469; Dr. Muhammad Kamran SiddiquiIn this dissertation, we calculated topological indices named ve-degree Zagreb alpha index, first ve-degree Zagreb beta index, second ve-degree Zagreb beta index, ve degree Randic index, ev-degree Randic index, ve-degree atom-bond connectivity index, ve-degree geometric-arithmetic index, ve-degree harmonic index and ve degree sum-connectivity index for Path graph, Cycle graph, Fan graph, Friendship graph, Complete graph, Jahangir graph, Generalized Petersen graph, Circulant graph, Sun graph, Wheel graph and Cartesian product of graph. In addition, we compared results of topological indices for each graph separately and represented it graphically.Item 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