PhD
Permanent URI for this collectionhttps://repository.cuilahore.edu.pk/handle/123456789/50
This collection archives the complete set of theses produced by students of the COMSATS University Islamabad, Lahore Campus.
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Item Algebraic Characteristics of Graphs(Library Information Services COMSATS University Islamabad Lahore Campus, 2020) Muhammad Asim Razzaq; FA13-PMATH-004; LHR TP 7454; Dr. Kashif AliGraph theory is a vital and special branch of discrete mathematics. It deals with geometric computational study of various objects. The main component and object of the theory is graph and its generalization approach. Therefore, it has vast application to other mathematical and provides computational assistance to non-mathematical sciences. The most prominent use of graph theory as a significant tool in chemistry, this branch is named as chemical graph theory. It provides helpful assistance for obtaining molecular descriptor to develop essential relationship between molecular graphs and chemical compounds. Graph theory also serves its specialization in algebraic graph theory specifically labellings. In this dissertation, we formulate and discuss all these types of indices. We develop a new approach to calculate the eccentricities of vertices of any graph by using computer aid softwares. This approach help us to find the exact expression of the ECI and ABC5 for the butterfly, bene and torodial grid graphs. We also express a new type of counting polynomial associated with the previous counting polynomials. Moreover, we work some topological indices relative to degree dependent on generalized subdivision of line graphs. We also determine the general results about subdivision of line graphs for neighborhood valency-based indices. We also discuss the stability of line graph of chemical molecules.”Line0graphs furnish0a tool for0studying the0topological properties of0alpha-systems.”In addition to this, we study four important counting polynomials called omega, theta, PI and Sadhana for V-Phenylenic. We also introduced a new polynomial Upsilon on the basis of ”co” relation and find new results relative to new counting polynomial.”We also determine that inertia indices for V-phenylenic nanotube and these indices are not0equal for the line0graph of V-phenylenic0nanotube. We also find that the0nullity for this0nanotube and of line0graph of these0nanotube.”Lastly, we also discuss H-group magic labellings of some graphs. We mainly study about the H-groupmagic0total graph0labelings G(v; e) over finite0abelian0group Zt Zv, where H =K2; Ct and e = (t 1)v:Item Dynamical Properties of Specific Black Holes(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2017) Muhammad Umair Shahzad; FA13-PMATH-005; LHR TP 5606; Dr. Abdul JawadThe present thesis comprises the study of three dynamical phenomenon such as thermal fluctuations, accretion and tidal forces of black holes/regular black holes. We consider the logarithmic corrected entropy in order to analyze the thermal fluctuations. We examine the effects of thermal fluctuations on a regular black hole of the non-minimal Einstein-Yang-Mill theory with gauge field of magnetic Wu-Yang type and a cosmological constant. We investigate the first law of thermodynamics in the presence of logarithmic corrected entropy and non-minimal regular black hole. Furthermore, we discuss the thermal fluctuation problem by utilizing the higher order corrected entropy. We examine the thermodynamical behavior of two well-known black holes such as Reissner-Nordström Anti de Sitter black hole with global monopole and f(R) black hole in the presence of higher order corrected entropy. We also discuss the accretion problem in two phases. In first phase, we analyze the accretion onto static spherically symmetric regular black holes for specific choices of the equation of state parameter. The underlying regular black holes are charged regular black holes using the Fermi-Dirac distribution, logistic distribution, non-linear electrodynamics, respectively, and Kehagias-Sftesos asymptotically flat regular black holes. In second phase, we develop the Hamiltonian dynamical system to tackle the accretion problem. We investigate the accretion of test fluids onto regular black holes such as Kehagias-Sftesos black hole and regular black holes with Dagum distribution function. We analyze the accretion process when different test fluids are falling onto these regular black holes. The behavior of fluid flow and the existence of sonic points is being checked for these regular black holes. Finally, we investigate the tidal forces occurring in a Kiselev black hole surrounded by radiation and dust fluids. We also solve the geodesic deviation equation for radially free-falling bodies toward Kiselev black hole. We explain the geodesic deviation vector graphically and point out the location of the event and Cauchy horizons for specific values of the radiation and dust parameters.