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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On the LCM Lattice of Powers of Monomial Ideal in Three Variables
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) MUHAMMAD WAQAR BASHIR; CIIT/SP20-RMT-016/LHR; Dr. Sarfraz Ahmad; LHR TP 7630
Commutative algebra, graph theory, algebraic geometry and combinatorics, semigroup rings and combinatorial optimization, integer programming, and other fields are all related with monomial algebra. Suppose K is a field, S = K[x1, ..., xn] is a polynomial ring with n number of variables, lcm(J), the LCM lattice of J, may be constructed for each mono- mial ideal J ⊂ S = K[x1, ..., xn]. We categorise the powers of monomial ideals in terms of their qualities in terms of LCM lattices. The lcm lattice of the ideal J created by a set of monomials is defined as a lattice with every member being a least common multiple of generating set of J. In particular, we discuss about powers of monomial ideal and staircase of monomial ideal in three variable. The powers and products of monomial ideals in poly- nomial rings are the subject of this thesis. On the polynomial ring K[x1, x2, x3], we derive conditions for the power of monomial ideals. The powers of monomial ideals are easier to calculate when the requirements are met.
On Expected Values of Some Chemical Indices in the Random Phenylene Chains
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) MUNEEBA; CIIT/FA19-RMT-063/LHR; Dr. Sarfraz Ahmad; LHR TP 7426
Chemical graph theory is an interdisciplinary ﬁeld where the molecular structure of a chemical compound is analyzed as a graph. In recent years, numerous chemical indices have been proposed. In this thesis, we determine some topological indices and the ex- pected values of these indices. We explore some indices known as the Zagreb indices (including redeﬁned forms of the Zagreb indices), the forgotten topological index, the reduced reciprocal Randic index and the reduced second Zagreb index of some random Phenylene and the random Cyclooctane chains. Later this, we look at the Zagreb Con- nection indices of some metal trihalides. Moreover, we make a comparison among the expected values of these indices and give a graphical representation respecting these ran- dom chains and metal trihalides.
On Tchebyshev Subdivision of Simplicial Complexes
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2018) Iqra Siddique; CIIT/FA16-RMT-035/LHR; Dr. Sarfraz Ahmad; LHR TP 5197
In this work, we studied the Tchebyshev subdivision of a simplicial complex Δ as combinatorial and algebraic point of view. In particular, we have studied f-vector and h-vector transformation maps and properties of corresponding transformation matrices. We have also studied the impact of this subdivision on the algebraic properties of the corresponding Stanely Reisner Rings IΔ, including dimension, primary decomposition and Hilbert series. We extended these results to some other subdivisions of a simplicial complex Δ.
Topological Descriptors of OTIS Interconnection, Block Shift and Hierarchical Hypercube Networks
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) Iftikhar Ahmed; CIIT/FA14-PMATH-003/LHR; Dr. Sarfraz Ahmad; LHR TP 7453
Topological Indices(TIs) are the numbers associated with the graphs of chemical compounds/networks that help us understand their properties. The aim of the present work is to compute TIs of OTIs swapped networks, Hierarical hypercube networks and block shift networks. Some of the TIs are computed directly and some are computed indirectly. For indirect computations the M-polynomial has been used. The M-polynomial contains key facts about degree dependent TIs, that is why it is so important. We compute Hosoya polynomials, Harary polynomials, Wiener index, modified Wiener index, Hyper Wiener index, Harary index, generalized Harary index, multiplicative Wiener index, M-polynomials, first Zagreb index, second Zagreb index, modified second Zagreb index, generalized Randi\'c index, inverse Randi\'c index, symmetric division index, Harmonic index, inverse sum index, augmented Zagreb index, Redefined first second and third Zagreb index and Zagreb type polynomials of networks mentioned above. We also computed irregularities, multiplicative version of different TIs . Our results can help the discovery of new medicines and in development of new software.
On Degree Based Banhatti Indices Of Some Graphs
(Library Information Services COMSATS University Islamabad Lahore Campus, 2021) Faheem Yaseen; FA19-RMT-043; LHR TP 7444; Dr. Sarfraz Ahmad
In the domains of electronic and electrical engineering, graph theory is crucial. It’s significant in signal processing, networking, communication theory, and a variety of other fields. A topological index (TI) is a numerical value that correlates chemical networks with physical and chemical qualities, as well as chemical reactivity. In this thesis, we compute first and second Banhatti Indices, first and second K-hyper Banhatti indices, first and second multiplicative K-Banhatti indices, first and second multiplicative K-hyper Banhatti indices, K-harmonic Banhatti indices, multiplicative K-harmonic Banhatti indices for certain graphs like as Hierachical hypercube network one and two, block shift network one and two, Octagonal network and line graph of wheel graph. My thesis comprising of four chapters. In the first chapter we define some fundamental definitions. In the 2nd chapter, we find Banhatti indices for Hierachical hypercube network one and two, block shift network one and two. In the 3rd chapter, we find Banhatti indices for Octagonal network and line graph of wheel graph. In the 4th chapter, we present the conclusion of our thesis. In the last, we present the references of our thesis.
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 Ahmad
A 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.
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 Ahmad
The 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.
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 Ahmad
A 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).
On lcm Lattice of Edge Ideals associated to Cycle and Complete Graphs
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) Alia; SP19-RMT-008; LHR TP 6468; Dr. Sarfraz Ahmad
On Some Topological Indices and Algebraic Properties of the Polyomino Chains of 4K-Cycles
(LHR TP 6988, 2016) Farah Iqbal; SP15-RMT-007; LHR TP 6988
In the present age of science and technology, topological indices have sig nificant role in the study of Quantitative Structure-activity (QSPR) and Structure-property (QSPR) relationships, to understand the chemical prop erties of the chemical compounds. In mathematical chemistry distance-based molecular descriptors are used to depict the structure of various molecules. For a simple connected graph G=(V,E), the Harary index is described as the sum of reciprocals of dis tances between all pairs of the vertices of the graph G. In this work, we derived some conjectures about the Harary index of the linear polyomino chain of 4k-cycles provided that k = 2 for both the cases i.e. linear and zig-zag chains, also there are expressions to get the sum of distances of the vertices while keeping one vertex as fix by dividing the chain into four dif ferent levels. This technique provide a basis to extend the idea for some other values of k

M.Phil / MS

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