On Strong Fuzzy Resolving Set of Fuzzy Wheel Graphs

Let Image be a fuzzy set on Image. A fuzzy labeling graph Image is a graph with bijective membership functions Image and Image so that each vertex’s membership degree and every edge’s membership value are different. Further, it satisfies Image for Image. “A graph formed from a single vertex connected to the vertices of a cycle of length Image is called a wheel graph with Image vertices". In this paper, we construct an algorithm for fuzzy labeling of wheel graphs. Under the algorithm, we have the degrees of vertices and edges are different and the monotone decreasing. The vertex Image gets the biggest degree among other vertices. Further, the edge Image is assigned to the biggest degree, and Image obtains the smallest degree. We also show the “strength of connectedness" between vertices in the fuzzy wheel graph. Finally, we investigate the “strong fuzzy resolving set" (SFRS) of the fuzzy labeling wheel graph with Image vertices and get the strong resolving number Image.