M.Phil / MS

Permanent URI for this collectionhttps://repository.cuilahore.edu.pk/handle/123456789/52

This collection archives the complete set of theses produced by students of the COMSATS University Islamabad, Lahore Campus.

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2018 - 20202

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Author: search.filters.author.Dr. Hafiz Muhammad Afzal Siddiqui, Assistant ProfesorSubject: search.filters.subject.department of mathematics

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    Computing Metric Dimension of M-Level Wheel Related Graphs
    (Library Information Services, COMSATS University, Lahore Campus, 2018) Ayesha Razzaq,; SP16-RMT-010; Dr. Hafiz Muhammad Afzal Siddiqui, Assistant Profesor; LHR TP 5332
    An ordered subset set for of nodes of is called a resolving set or locating if each node is individually determined by its code of distances to the nodes in . A resolving set of minimum number of nodes is called a basis for and this cardinality is the metric dimension or location number of , represented as In this thesis, we compute the metric dimension of some wheel related graphs, such as m-level gear graph, m-level antiweb-wheel graph, m-level antiweb-gear graph and an infinite class of convex polytopes denoted by respectively. We prove that the metric dimension of aforementioned wheel related graphs and a family of convex polytope is not bounded. The unbounded metric dimension of convex polytope also furnish a negative answer to the problem given in [19]: Open Problem: “Is it the case that the graph of every convex polytope has constant metric dimension?” It is natural to ask for characterization of graphs with unbounded metric dimension.
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    On Metric Dimension - Edge Metric Dimension
    (Library Information Services, COMSATS University, Lahore Campus, 2020) Muhammad Rafiullah,; FA18-PMAth-001; Dr. Hafiz Muhammad Afzal Siddiqui, Assistant Profesor
    On Metric Dimension - Edge Metric Dimension and Topological Properties of Connected Graphs The distance between any two vertices of a connected graph is the length of a shortest path between them. Any two vertices/edges are said to be resolved by a vertex if they have different distances w.r.t. that vertex. A set is a resolving set/edge resolving set if every vertex/edge of is resolved by some vertices of , respectively. A topological index is a real number associated to a graph that describes its topological properties. The main objective of this thesis is to study edge metric dimension of certain families of wheel related graphs and generalized Petersen graphs . It has been proved that the gear graph, the fan graph, the friendship graph, the sunflower graph and certain convex polytopes have unbounded edge metric dimension whereas the generalized Petersen graph has a constant edge metric dimension. An explicit Matlab program has also been given to generate the edge resolving set and edge coding for generalized Petersen graphs A comparative study between the metric dimension and the edge metric dimension of the aforementioned families of graphs has also been conducted. The second part of the thesis studies the Zagreb and co-Zagreb indices of iterated strong double graphs and some eccentricity-based indices of Sierpinski graphs and their regularizations. Moreover, some explicit algorithms have also been given to verify the validity of the results. x
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