Browsing by Author "Dr. Muhammad Hussain, Assistant Profesor"

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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.
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
Valuations and Metric Dimensions on Graphs
(Library Information Services, COMSATS University, Lahore Campus, 2016) Shahid Imran,; LHR TP 5605; FA12-PmAth-003; Dr. Muhammad Hussain, Assistant Profesor
Labeling of graph is a beautiful and rich technique of Mathematics. It has extensive usage in applications such as data transmission, x-ray, circuit design, astronomy, communication links and coding theory. Labeling of graph is defined as a correspondence from the set } , ,3,2,1{ f e v    to the vertices, edges and faces of a plane graph G in such a way that each vertex, edge and face receives exactly one label and each number is used exactly once as a label. The weight of a face under a labeling of type )1,1,1( is the sum of labels carried by that face and all the edges and vertices surrounding it. A labeling of type )1,1,1( of a plane graph G is called d-antimagic if for every positive integer s the set of weights of all s-sided faces is } )1 ( , , 2 , , { d f a d ad aa      for some integer a and 0d , where f is the number of s-sided faces. In particular when 0d then the d antimagic labeling of type )1,1,1( is called magic labeling of type )1,1,1( . Moreover, if the vertices are labeled by the smallest possible number. It is known as super magic and anti magic accordingly. Furthermore, let G be a connected graph and ) , ( y x d be the distance between the vertices x and y in G. A set of vertices W resolves a graph G if every vertex is uniquely determined by its vector of distances to the vertices in W. A metric dimension of G is the minimum cardinality of a resolving set of G and is denoted by ). ( dimG This dissertation studies about the construction of super face anti-magic labeling of type )1,1,1( for disjoint union of toroidal fullerenes, magic and anti-magic labeling of type )1,1,1( for union of generalized friendship graphs. Metric dimension of Jahangir related graphs, generalized prism related graphs and graphs obtained by rooted product has been also calculated.