Department of Mathematics

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Author: search.filters.author.Dr. Muhammad Hussain, Assistant ProfesorSubject: search.filters.subject.department of mathematics

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    Magic Labeling of Cycle Like Graphs
    (Library Information Services, COMSATS University, Lahore Campus, 2019) : Rabia Bibi; , FA17-RMT-016; Dr. Muhammad Hussain, Assistant Profesor; LHR TP 5652
    Graph labeling is play very vital role in graph theory applications like network addressing of communication, X-ray, circuit designing, crystallography, radar, missile guidance, astronomy and data base management. A labeling is bijective mapping in which natural number are assigned to vertices or edges. If weights of all vertex have same sum, such labeling is called magic labeling. The notion of (a, d) vertex-antimagic-total labeling was introduced by Baca et al. [5] in 2000. A labeling in which domain set consists of all vertices and edges is called total labeling. A labeling is called super (a, d)-vertex antimagic-total labeling (VAMTL) if we allot smallest number to vertices and then to edges. Hussain et al. [17, 18] formulated (a,d)-vertex antimagic total labeling on Harary graphs, however, many cases are still open. This dissertation learning about the configuration of new results of vertex-magic total labeling and (a,d)-vertex antimagic total (VAT) labeling of Harary graphs. Also we construct same new results of super (a, d)-vertex antimagic total (VAT) labeling on Harary graphs.
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    Topological Indices Of Chemical Graphs
    (COMSATS University Islamabad, Lahore Campus Library Information Services, CUI Lahore, 2018) Sahar Dilber,; SP14-BSM-002; Dr. Muhammad Hussain, Assistant Profesor; LHR TP 5262
    Topological indices are real numerical parameters of a molecular structural net works and structural networks. These networks are characterize its topology and graph invariant. The molecular networks plays a vital role in QSAR \QSPR study, phisco-chemical properties and topological indices like Randic, atom-bond connec tivity(ABC) and geometric-arithmetic(GA) are used to diagnose the bioactivity of chemical compounds. Actually these topological indices is designed by transforming a chemical structure into a numeric number. In the area of research graph theory has been found to be very useful. In this thesis, we will compute the degree based topological indices the so-called general Randic index Rγ(G) for γ = {1, 12−1,−12 },atom bond connectivity(ABC), geometric-arithmetic(GA), first Zagreb, second Zagreb, second modified Zagreb, third zagreb, hyper Zagreb and augmented zagreb topological indices for subdivision of dif ferent kinds of networks like sierpinksi s(n,k) networks as well as molecular structural networks. This study will give us a very interesting and different results by using new topological index that is first Zagreb, second Zagreb, second modified Zagreb, third zagreb, hyper Zagreb and augmented zagreb topological indices