Abstract:
The aim of the thesis is to investigate the algebraic properties of fuzzy graphs with particular 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 relationships 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 commutative algebra.
