Department of Mathematics

Permanent URI for this communityhttps://repository.cuilahore.edu.pk/handle/123456789/21

Browse

Subject: search.filters.subject.Dr. Muhammad Faisal Nadeem

Search Results

Now showing 1 - 6 of 6
  • No Thumbnail Available
    Item
    Mittag-Leffler Theorem and Series Representation of Meromorphic Functions
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Muhammad Waseem Akram; CIIT/FA19-RMT-002/LHR; Dr. Muhammad Faisal Nadeem; LHR TP 7404
    The goal of this thesis is to present a complete proof of Mittag-Leffler theorem, and to present some applications. We first give a simpler proof, valid for open disks and the whole complex plane. This proof uses in a crucial way the approximation of holomorphic function by means of polynomials on such domains, by means of their Taylor series. The proof of Mittag-Leffler theorem for an arbitrary domain G ⊂ ℂ is much more involved and requires the development of a more general theory of approximation of holomorphic function on complex domains. We present this theory and prove Runge’s theorem, a fundamental result in complex analysis providing conditions to have the required approximations. This allows us to complete the proof of the general version of Mittag-Leffler theorem. We complete this thesis by presenting some applications of the above results.
  • No Thumbnail Available
    Item
    Fault Tolerance Metric Dimension of Biswapped Graph
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Muhammad Navid Alam; CIIT/FA19-RMT-090/LHR; Dr. Muhammad Faisal Nadeem; LHR TP 7401
    The biswapped networks is a new interconnection networks in multiprocessor systems. These are networks of devices or processors and connection of these devices or processors. Here network can be expressed in the form of graph. Devices or processors represent vertices (nodes) and connection of devices or processors represent edges (links). The subset of the nodes set is called the resolving set if all the representations are different. The minimum cardinality of resolving set is called the locating number or metric dimension. If after the removal of any vertex from the resolving set the set remain the resolving set then the set is called fault tolerant resolving set and the minimum cardinality of this set is called fault tolerant metric dimension. In this article we found the fault tolerant metric dimension of biswapped graph.
  • No Thumbnail Available
    Item
    On Metric Dimension of Biswapped Networks
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Waqar Ali; CIIT/FA19-RMT-099/LHR; Dr. Muhammad Faisal Nadeem; LHR TP 7384
    The biswapped networks is a new interconnection networks in multiprocessor systems. These are networks of devices or processor and connection of these devices or processors. Here network can be expressed in the form of graph. Devices or processors represent vertices (nodes) and connection of devices or processors represent edges (links). The subset of the nodes set is called the resolving set if all the representations are different. The minimum cardinality of resolving set is called the locating number or metric dimension. In this article we found the locating number of different types of interconnection networks. We found the exact value of locating number for biswapped networks developed by different basic graphs like, path, cycle, and power graph of path graph.
  • No Thumbnail Available
    Item
    On Topological Co-Indices of Chemical Graphs
    (Library Information Services COMSATS University Islamabad Lahore Campus, 2021) Muhammad Farhan Hanif; FA19-RMT-018; LHR TP 7412; Dr. Muhammad Faisal Nadeem
  • No Thumbnail Available
    Item
    Degree Base Topological Indices of Metallic Organic Compound
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) Abdul Qadeer; FA18-RMT-064; LHR TP 6463; Dr. Muhammad Faisal Nadeem
    A topological index describes the chemical information as numerical number. Topological index is a graph invarient and describe the topology of that graph. In development of QSARs(quantitative structure-activity relationships) topological indices are very useful. QSARs relates biological activity of a molecule with its chemical structure. QSAR are useful in toxicity prediction and in drug discovery. There are some types of topological indices like degree-based topological indicex, distance-based topological indicex, eigen value toplogical indicex and matching and mixed topological index. There are some famous toplogical indices like geometric-arithmetic index, Randić index which have many applications in chemistry and useful in pharmacology, ABC index(achivements of babies and children). In this thesis we discuss the metallic non-metallic behaviour of TM-TCNB graph. We compute topoligical indices ABC index, geometric arithmetic index and Randić index for variation of alpha. We also calculated sum connectivity index and symmetric division index for different results. In this thesis there are six chapters. In first chapter we will define some funddamental definitions. In 2nd chapter we will discuss different types of topological indices like Hosoya index, Winner index Estrada index etc. 3rd chapter is related to literature review of TCNB graph. In 4th chaper there is basic structure of TCNB and results of TCNB graph. Conlcusion and relevant refrences are given in 5th and 6th chapters respectively.
  • No Thumbnail Available
    Item
    On Statistical Analysis of Topological Indices for Iron Disulfide Network
    (Library Information Services COMSATS University Islamabad Lahore Campus, 2025) Saba Hanif (FA23-RMT-035); Dr. Muhammad Faisal Nadeem; LHR TP 9781
    The 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 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, the hyper Zagreb index, the forgotten index, the augmented Zagreb index, the Balaban index, and redefined Zagrebtype indices, of Iron Disulfide Network FeS2. Afterwards, we found the physical measures like heat of formation of the iron disulfide Network FeS2. Then, we fitted curves between different indices and corresponding heats 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. 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 Disulfide NetworkFeS2