The Cartesian and Composition Products of Distance-Hereditary Fuzzy Graphs

Fuzzy graphs serve as a valuable tool in mathematics, enabling professionals to effectively depict fuzzy relationships among various entities. The inherent property of fuzziness is advantageous in numerous contexts, helping to forecast and address issues. Distance-Conserving Graphs are connected graphs distinguished by the property that all induced paths preserve isometry. Many real-world problems are complex and frequently involve ambiguous information. By integrating Distance-Hereditary graphs with fuzzy sets, we introduce a novel concept. In this paper, we thoroughly examine and introduce operations on Distance-Hereditary Fuzzy Graph, which will explore cartesian and composition products related to Distance-Hereditary Fuzzy Graphs.