Fuzzy F-index of fuzzy zero divisor graphs with MATLAB based algebraic applications

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 (briefly FF-index) has been formulated theoretically for the fuzzy zero divisor graphs of the commutative ring Z(n), where n = & wp;(alpha), & wp;1 & wp;2, & wp;(2)(1)& wp;2, & wp;(2)(1)& wp;(2)2, & wp;1 & wp;2 & wp;3 (& wp;1, & wp;2, & wp;3 are primes and alpha >= 3). 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 zero divisor graphs for every non-prime value of n > 1.