Browsing by Author "Shahid Imran,"

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    Structural Properties Of Certain Molecular Graphs
    (COMSATS University Islamabad, Lahore Campus Library Information Services, CUI Lahore, 2018) Shahid Imran,; FA14-BSM-017; Dr. Muhammad Hussain, Assistant Profeso; LHR TP 5261
    Abstract Let G=(V,E)beasimple connected graph. The sets of ver tices and edges of GaredenotedbyV =V(G)andE =E(G) respectively. In such a simple molecular graph, vertices rep resent atoms and edges represent bonds. In chemical graph theory, we have many invariant polynomials and topological indices for molecular graph. In this thesis we focus on the structure of molecular graph of Bakelite network. Morever the vertices having degrees (2,2),(2,3) and (3,3) gives the generalized form of count of edges in terms of m and n. The m in chemical structure represent the number of rows and n represent the number of column in Bakelite structure. In this thesis we compute the different indices such as Atom bond conecctivity ABC,Geometric arithmatic G(A), Zagreb, Hyper Zagreb, Augmented Zagreb, Randic index and Har monic indices of Bakelite network. Topological indices are real numerical parameter of a chemical structural networks and structural networks. These networks are characterize its topology and graph invariant. The topological indices like Randic, ABC, G(A), are used to diagnose the bioactiv ity of chemical compounds. Actually these topological in dices is designed by transforming a chemical structure into a numeric number. i
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    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.