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 Total Labellings of Some Connected Graphs(Library Information Services, COMSATS University, Lahore Campus, 2019) SP17-RMT-014; Mujahid Shehzad,; Dr. Kashif Ali, Assistant Profesor; LHR TP 5428Ashraf et al. in [3] introduced the concept of vertex H irregular labelling and edge H irregular labelling. Let H be sub graph of given graph G. If each edge of graph G is contained in any subgraph Hi where i ={ 1,2,3,…, k } of G and if each Hi is isomorphic to given subgraph H. then the collection Hi of subgraphs of G is said to be H-covering of G. They also introduced the concept of edge H irregular strength ehs(G) that is the minimum k for which the graph has total H irregular k labelling and vertex H irregular strength vhs(G) that is the minimum k for which the graph has total H irregular k labelling The thesis is devoted to study the total vertex C3 irregular strength wheel graph and triangular ladder graph taking subgraph C3. We also found the total vertex C4 irregular strength ladder graph and grid graph. Furthermore, we find the total vertex C8 irregular strength of a connected graph Qn.Item Degree-Distance Base Topological Indices from Some Graphs Operations(Library Information Services, COMSATS University, Lahore Campus, 2019) Aqib Ali,; SP17-RMT-002; Dr. Kashif Ali, Assistant Profesor; LHR TP 5420Degree-Distance Base Topological Indices from Some Graphs Operations In this thesis, firstly we find the degree based topological indices and M-polynomial for line graph of t-subdivided graphs of probabilistic neural networks L[PNN(q,c∗,c)] for t ≥1. Wealso find the fourth and fifth version of atomic bound connectivity ABC4, ABC5 index and fourth and fifth version of geometric-arithmetic GA4, GA5 index of line graph of 1-subdivided graphs of probabilistic neural networks L[PNN(q,c∗,c)]. Secondly, we find the degree based topological indices and M-polynomial for line graph of m-subdivided graphs for the chain of Bismuth Tri-Iodide L[m−Bil3] for m ≥ 3. Lastly, we find the first and third zagreb eccentric index and M-polynomial of sierpinski networks S(n,k).Item Cycle Labelings and Eccentric Base Invariants of Graphs(Library Information Services, COMSATS University, Lahore Campus, 2016) By: Muhammad Azeem,; FA14-BSM-014; Dr. Kashif Ali, Assistant Profesor; LHR TP 5259A simple graph G admits an H-covering if each edge in E(G) is a member of a sub graph of G isomorphic to H. An H-magic labeling λ of a graph G possessing an H-covering is a bijective function from the vertex-set and the edge-set of the graph Gonto the set {1,2,...,|V(G)|+|E(G)|} with a property that for every subgraph H of G isomorphic to H, the sum wtλ(H) = ∑ v∈V(H) λ(v)+ ∑ e∈E(H) λ(e) is equal to µ. The sum wtλ(H) is termed as, the H-weight. A graph is called H-supermagic if it possesses an H-supermagic labeling. Let G be a graph and v be a vertex of G. The eccentricity of the vertex v is the maximum distance from v to any vertex. That is, e(v) = max{d(v,w) : w ∈V(G)}. Firstly, we find the C4-supermagic labelings for the disjoint union of non-isomorphic copies of ladder graph, which are the generalization of the result proved in [21]. Moreover, we find the newclasses of 2-self centered graph namely uniform subdivided complete bipartite Kk n,m graph and line graph of uniform subdivided complete bipar tite graph L(Kk n,m). We also find their distance base topological indices of Kk n,m and L(Kk n,m). Then we also find eccentricity of uniform subdivided wheel graph, line graph of uniform subdivided wheel graph and their distance based topological indices