Farah IqbalSP15-RMT-007LHR TP 69882026-03-122016https://repository.cuilahore.edu.pk/handle/123456789/2757In the present age of science and technology, topological indices have sig nificant role in the study of Quantitative Structure-activity (QSPR) and Structure-property (QSPR) relationships, to understand the chemical prop erties of the chemical compounds. In mathematical chemistry distance-based molecular descriptors are used to depict the structure of various molecules. For a simple connected graph G=(V,E), the Harary index is described as the sum of reciprocals of dis tances between all pairs of the vertices of the graph G. In this work, we derived some conjectures about the Harary index of the linear polyomino chain of 4k-cycles provided that k = 2 for both the cases i.e. linear and zig-zag chains, also there are expressions to get the sum of distances of the vertices while keeping one vertex as fix by dividing the chain into four dif ferent levels. This technique provide a basis to extend the idea for some other values of kenDr. Sarfraz Ahmadsp15Department of MathematicsMathematicsAlgebraic PropertiesPolyominoThesis