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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Item Structural Analysis and Comparisons of Identity Graph of Groups(Library Information Services COMSATS University Islamabad Lahore Campus, 2025) Muhammad Sufyan (FA23-RMT-029); Dr. Hani Shaker; LHR TP 9775The identity graphs of three groups are examined in this thesis: the quaternion group Q8, the symmetric group S5, and the alternating group A4. Every group element in an identity graph is a point (vertex) that is connected to both the identity and its inverse. We compare these graphs by examining fundamental characteristics such as the number of connections and points, triangles, self-inverse elements, and special groupings within the graph. Our research demonstrates how these graphs provide a clear and visual understanding of the group structure. This work proposes new techniques to use graphs to study groups by tying together concepts from group theory and graph theory. Due to vast usage of networks, numerous networks are considered and widely practiced in several branches of science, i.e in engineering, chemistry, biology, and computer networking. Networks can be describable in the aspect of graphs, where a vertex is affiliated with a node, and the connection between them as edgesItem Spanning Simplicial Complex of Certain Family of Graphs(Library Information Services COMSATS University Islamabad Lahore Campus, 2025) Zain Ul Abideen (FA23-RMT-053); Dr. Hani Shaker; LHR TP9796The spanning simplicial complex Ds(Gw) related to a family of graphs known as w-wing graphs is thoroughly examined in this thesis. The combinatorial essence of cycle-free edge subsets is captured by Ds(Gw), where each facet corresponds to a spanning tree of the graph Gw. We examine this complex’s combinatorial invariants, which together carry significant structural information. These invariants include the f -vector, Euler characteristic, and Hilbert series. In addition, we investigate the algebraic features of the Stanley–Reisner ring of Ds(Gw) and define and analyze the facet ideal. In addition to generalizing existing concepts, the results provide a tangible link between commutative algebra and combinatorial topology.