Mubeen NazSP23-RMT-017Dr. Imran AhmedLHR TP 95792026-03-182024-03-18https://repository.cuilahore.edu.pk/handle/123456789/2936The aim of the thesis is to investigate the algebraic properties of fuzzy graphs with par ticular focus placed on three main topics which are the square of a graph, minimal free resolutions of modules, and fuzzy edge ideals. We will examine the fuzzy graphs relation ships to fundamental algebraic concepts like rings, ideals, and edge ideals by examining their structural and algebraic characteristics. The study focuses on how graph-theoretical concepts and algebraic methods work together. It gives information about minimal free resolutions and the behavior of fuzzy square graph and edge ideals of fuzzy square graph. These results advance the theoretical underpinnings and practical uses of fuzzy commuta tive algebraenDepartment of MathematicsMathematicsSP23investigatealgebraic propertiesfuzzy graphsThesis