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 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 Modelling And Analysis Of The Outbreak Of COVID-19(Library Information Services COMSATS University Islamabad Lahore Campus, 2021) Waseem Shokat; FA19-RMT-009; LHR TP 7433; Dr. Sadia ArshadMathematical models provide different strategies to control different diseases. The way toward building up a mathematical model is named mathematical Modelling. We develop different models that estimate the course of infection COVID-19 to help through a viable control system and effectiveness of vaccine by using data of Saudia Arabia, Italy, Canada and Pakistan via fractional order q. These model of epidemiologic analysis to predict that how COVID-19 spread and how we can control outbreak of this virus by using basic reproduction number R0. Special consideration is given to the worldwide elements of the equilibria, positiveness, boundedness and stability analysis. For stability if R0 < 1, an infected person transfer the disease individually in new infected is less than one on average over the lifetime of its infectious time, and the infection cannot spread. On the other hand at endemic equilibrium point if R0 > 1, then disease transfer from each infected person to more than one new infection on average and the disease will spread across the population. Sensitivity of models will be studied in different variations of parameters, focusing in particular on parameters that may arise. Moreover, the fitting of parameters through least squares curve fitting technique is performed. Finishing the worldwide disease lacks usage of various precaution, counting civil Separating, contact, testing following and more people should be vaccinated.Item Multiple Lump And Rogue Wave Solutions For …(Library Information Services COMSATS University Islamabad Lahore Campus, 2021) Muhammad Aamir Ashraf; FA19-RMT-092; LHR TP 7421; Dr. Sarfraz AhmadA solitary wave is a localised “wave of transcription” that appears from a balance between dispersive and nonlinear effects. A soliton is a specific type of solitary wave, since it maintains its original shape and speed when collides with other solitons. Nonlinear evolution equations (NLEEs) are the main classification of soliton solutions. In this work, our purpose is to attain lump, lump with one and two-kink soliton, periodic– waves, rogue–waves solution for various forms of NLEEs. We’ll also obtain M-shaped rational soliton, M-shaped interactions with kink and periodic waves, periodic-cross kink solutions, homoclinic breather and multi–wave solutions. In this thesis, we’ll study various forms of NLEEs to attained these types of solutions by the combinations of bilinear, hyperbolic, trigonometric, exponential, and hyperbolic functions. We also seen the degenerations of hybrid waves, through some fittingly bilinear forms and also discussed graphical behavior of our system.Item On Some Partitions Of The Multicomplexes(Library Information Services COMSATS University Islamabad Lahore Campus, 2021) Ali Shan; FA19-RMT-088; LHR TP 7418; Dr. Sarfraz AhmadThe study of monomial ideal of polynomial ring ’R’ at most with the pretty clean three variables is done. The polarisation I p is known as clean If and only if, the arbitrary monomial ideal ’I’ is also relatively clean. A proper revised characterisation is prettyclean along the monomialideals in theterms of arithmetic degree is presented. This means that a simplicial complex’s polarisation corresponds to shellable if and only if a multicomplex is shellable. In this thesis Stanley decomposition with respect to prime filtrations is discussed.Item On Vertex Mostar Index of the Boron and Polyomino Chains(Library Information Services COMSATS University Islamabad Lahore Campus, 2021) NAJMA SHABIR; FA19-RMT-039; LHR TP 7420; Dr. Sarfraz AhmadA bond-additive topological invariant, known as the Mostar index, has been described as a measure of peripherality in networks and graphs. Later on, other index variations were created, including the edge Mostar index and the total Mostar index. Some experiments are done using vertex-Mostar index on boron nanotubes and polyomino chains but attained results are not good. Therefore, we show how a variation of the cut method described by Klavar, Gutman, and Mohar may be used to efficiently compute it for Honeycomb network H(m;n). We compute the vertex-Mostar index of Honeycomb network H(m;n). Moreover, We’ve also included results related the vertex-Mostar index of Honeycomb network H(m;n).Item On Magic Type Labeling of Some Families of Subdivided Stars(Library Information Services COMSATS University Islamabad Lahore Campus, 2021) HINA BIBI; FA19-RMT-049; LHR TP 7415; Dr. Hani ShakerA graph G is simple means it is undirected,does not contain any multiple edges and loop. In a directed, the direction of edges are given. The graph is con- nected if all the edges and vertices are given. A graph is said to be loop when starting and ending vertex is same. If we assigns positive integers to the set of nodes(vertices) and set of lines(edges) by a mapping that is bijection then it is known as labeling. If we assigns positive integers to set of nodes(vertices) only then the labeling become vertex(node) labeling. If we assigns positive in- tegers to set of lines(edges) then the labeling is known as edge(line) labeling. If we label the vertex(nodes) set and edge(lines) set both the resulting labeling is known as total labeling. There are many types of labeling but in this we will discuss about the magic type labeling. The terms edge label, edge sum and edge weights will help us to label the graph. In research magic and anti-magic labeling is growing fast. We will introduce new results on the basis of a concept labeling that is SEMTL of the families of subdivided star.