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 On Algebraic Aspects Of Spanning Complexes(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) Asif Allah Ditta,; FA17-RMT-027 Contributor(s):; Dr. Hani Shaker, Assistant Profesor [Supervisor]; LHR TP 5656Item On Characterization Of Spanning Forest Complexes(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2016) Muhammad Asif,; FA14-MSMAT-004; Dr. Hani Shaker, Assistant Profesor [Supervisor]; LHR TP 4636In this thesis, we discuss the algebraic and combinatorial aspects of spanning forest complex ∆s(G) associated to simple disconnected graph G. We mainly emphasis on disjoint union of isomorphic copies graph G and provide special importance to tCn where tCn is the disjoint union of t cycles of length n and call this graph t-cycle graph. We give the characterization of s(tCn), all spanning forests, of tCn. We intend to provide the algebraic and combinatorial characterization of spanning forest complex ∆s(tCn) associated to tCn. In particular, we compute the formula for the f-vector of spanning forest complex of t-cycle graph. We also compute the h-vector and Hilbert series of Stanley Riesner ring k[∆s(tCn)]Item Merrifield-Simmons Index Of Molecular Graphs(COMSATS University Islamabad, Lahore Campus Library Information Services, CUI Lahore, 2018) Noor-Un-Nisa,; FA16-RMT-014; Dr. Hani Shaker, Assistant Profesor [Supervisor]; LHR TP 5185The mainobjective of this thesis is to compute Merrifield- Simmons index of molecular graphs. The molecular graph that is taken for this purpose is V- phenlynic graph. The nanostructures under consideration are nanosheet G = V PHY[p,q] and H = VPHZ[p,q] nanotube. We compute the results for V- phenlynic nanosheet and nano tube. To compute Merrifield- Simmons index, first we find all independent sets of said graphs. We use the technique of transfer matrix to solve this problem. We develop some algorithms to compute Merrifield- Simmons index of said graphs. We construct a matlab program for the final results.