PERFECT S-GEODETIC FUZZY GRAPHS

This study introduces the concept of a Pseudo s-geodetic set within the context of fuzzy graphs. This set comprises all nodes that are not members of any s-geodetic basis for a given fuzzy graph G. The size of this set is termed the Pseudo s-geodetic number of G. We specifically define fuzzy graphs possessing a Pseudo s-geodetic number of zero as Perfect s-geodetic fuzzy graphs. Several examples of such graphs are provided. Furthermore, we demonstrate that complete fuzzy graphs with two nodes, as well as fuzzy cycles where each arc has identical strength, fall under the category of Perfect s-geodetic fuzzy graphs.