Department of Mathematics

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Author: search.filters.author.Prof. Dr. Muhammad HussainSubject: search.filters.subject.Chemical Structures

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    Topological Indices Based on Line Graph of Different Chemical and Non Chemical Structures
    (Library Information Services COMSATS University Lahore Campus, 2024-03-18) Sehrish Aslam; SP23-RMT-037; Prof. Dr. Muhammad Hussain; LHR TP 9572
    The utilization of graph theory has expanded considerably across various disciplines, with notable advancements in chemical graph theory. In recent years, researchers have explored numerous innovative avenues within this field. A chemical graph models a molecule by representing atoms as vertices and chemical bonds as edges. Analyzing topological indices, which are mathematical measures of a molecule’s structure, is crucial for understanding its physical and chemical properties. Firstly, we focused on degree-based topological indices, namely the Randic index, atom bond connectivity index, geometric arithmetic index, the first and the second Zagreb indices and co-indices, hyper Zagreb index, Hyper Zagreb index of Subdivision graph and Line graph of Niobium Dioxide NbO2.
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    Metric Dimension on Line Graph of Different Chemical Structures
    (Library Information Services COMSATS University Lahore Campus, 2024-03-17) Zunaira Ijaz; FA22-RMT-028; Prof. Dr. Muhammad Hussain; LHR TP 9387
    The Metric Dimension of a graph G is the minimum number of basis element in a resolving set. Let G = (V,E) be a connected graph and length of a shortest path between u and v is known as distance, denoted by d(u, v) in G. Let B = b1,b2,...,bk be an ordered set of vertices of G. The representation r(u|B) of u with respect to B is the k tuple (d(u,b1),d(u,b2),d(u,b3),...,d(u,bk), where B is called a resolving set or locating set if every vertex of G is uniquely identified by its distances from the vertices of B or equivalently if distinct vertices of G have distinct representations with respect to B. A resolving set of minimum cardinality is called a basis for G and cardinality is the metric dimension of G is denoted by dim(G). We investigated metric dimension on Line Graph of Polythiophene Network, Backbone Network, Hex-derive Network and Chain Sillicate Networ