Fuzzy and crisp computational analysis of certain graphs structures via machine learning techniques

In the evolving landscape of computer science and artificial intelligence, the integration of fuzzy graphs theory and topological indices offers a robust framework for decision-making processes. Fuzzy graphs, characterized by their capacity to handle uncertainty and imprecision, extend traditional graph concepts, enabling a more nuanced representation of complex networks. This study explores the application of fuzzy topological indices to ladder and grid graphs, which are foundational structures in network theory. Ladder graphs, resembling the rung of the ladder, and a grid graph, representing a mesh-like structure, are analyzed through the lens of fuzzy graph theory to extract meaningful insights that aid in decision-making. The fusion of fuzzy topological indices with these graph structures provides a powerful tool for evaluating network robustness, optimizing routes, and enhancing overall system reliability. This paper delves into the exploration of traditional topological indices, such as the Randić index alongside fuzzy topological indices and the fuzzy Zagreb index, specifically applied to ladder and grid graphs. We analyze the above-mentioned graphs via machine learning techniques and also give comprehensive statistical analysis. We find a strong correlation between the ladder and fuzzy ladder graph and also between the grid and fuzzy grid graph. Our findings show that if the values of the topological index in the crisp case of ladder graph and grid graph are known, then we can accurately predict the values of the fuzzy topological index of ladder graph and grid graph. The analysis of topological indices in both crisp and fuzzy graphs using machine learning techniques is an innovative approach that not only saves time but also provides a more comprehensive and precise evaluation.