Fuzzy F-index of Fuzzy Zero Divisor Graphs with MATLAB Based Algebraic Applications

Abstract

This article aims to explore the theoretical properties of topological descriptors used in fuzzy graph theory, which combines elements of graph theory and fuzzy set theory, within algebraic structures. For this purpose, fuzzy F-index has been formulated theoretically for the fuzzy zero-divisor graphs of the commutative ring Zn, where n = ℘α, ℘1℘2, ℘21℘2, ℘21℘22 , ℘1℘2℘3(℘1, ℘2, ℘3 are primes). In particular, a SageMath-based drawing algorithm that embodies the fuzzy graph structures of the rings is presented for application based convenience. Furthermore, a MATLAB-based code was created that directly calculate the fuzzy F-index of the fuzzy zerodivisor graphs for every conceivable value of n.