PhD
Permanent URI for this collectionhttps://repository.cuilahore.edu.pk/handle/123456789/50
This collection archives the complete set of theses produced by students of the COMSATS University Islamabad, Lahore Campus.
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Item FACE ANTI-MAGIC LABELINGS AND DEFICIENCY OF GRAPHS(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2016) Ali Tabraiz; FA12-PMATH-001; LHR TP 4824; Dr. Muhammad HussainLabeling of graph is a beautiful and rich technique of Mathematics. It has extensive usage in applications such as data transmission, x-ray, circuit design, astronomy, communication links and coding theory. A labeling of a graph is a mapping that carries some set of graph elements into (usually positive integers). An ) , ( d a face anti-magic total labeling of a graph, with p vertices, q edges and f faces, is a one-to-one mapping that takes the vertices, edges and faces into }, , , 2 , 1 { f q p such that the sums of the label on the edges, vertices and faces form an arithmetic progression starting at a and having difference . d An edge magic total labeling of a graph G is a one-to-one mapping from ) ( ) ( G E G V onto the integers }, , , 2 , 1 { q p with the property that there is an integer constant k such that k y xy x ) ( ) ( ) ( for any ). (G E y x Furthermore, the edge-magic deficiency of a graph , G ) (G is defined as the minimum non-negative integer n such that 1 K n G is edge-magic.Item Degree and Distance Based Parameters of Certain Graph Structures Zeshan Saleem Mufti(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) Zeshan Saleem Mufti; FA12-PMATH-006; LHR TP 5950; Dr. M. Faisal NadeemTopological indices are a rapidly developing area of research in graph theory. There are various topological indices such as degree-based topological indices, spectrum based topological indices and distance related topological indices. These topological indices correlate certain physico-chemical properties such as boiling point, stability of chemical compounds and many more. In this dissertation, we focus on degree based and spectrum based topological indices. Under the degree based topological indices, we study topological indices such Randic index, general Randic index, Zagreb index, general sum connectivity index, first and second multiple Zagreb indices, geometric index, atom bond connectivity index for para-line graphs of some chemical structures such as Phenylene, Anthracene, Benzenoid, Pentacene. Similarly, we study the spectrum based topological indices such as Estrada index for certain chemical graph structures such as Phenylene, Anthracene, Bi-smuth Tri-iodide, benzene ring embedded in P-type-surface in 2D network (BRE). Also we find the energy of above mentioned structures. We also discuss the notion of distance related parameters such as metric dimension and edge metric dimension. We compute the edge metric dimension for the barcycentric Subdivision of Cayley Graphs. Also we have studied the M-polynomial and entropy of generalized Sierpinski graphs.