On ss-paths and ss-distance in Fuzzy Graphs

The existence of a strongest x − y path and a strong x − y path in a connected fuzzy graph has been proved [2]. Here it is established that there is a strongest strong path (ss-path) between any two nodes in a connected fuzzy graph. Some properties of ss-paths and ss-arcs in a fuzzy graph are studied. Here we define the ss-distance between two nodes x and y as dss (x, y) = 1/CONN g(x, y) Using this metric we observe that every connected fuzzy graph is ss-selfcentered.

Also we prove that a connected fuzzy graph with respect to the δ- distance [2]viz, δ(x, y) = 1 − CONNG(x, y), is selfcentered.