Distance in Fuzzy Graphs: G-distance, µ -distance, - Distance, and Ss-distance

This work mainly focuses on different distance concepts in fuzzy graphs. The properties of ?- distance,µ -distance and g-distance are studied and defined ss-distance in a connected fuzzy graph. A study of g-distance in a fuzzy tree and its associated maximum spanning tree is carried out. Various types of degrees of a node and its properties in fuzzy graphs are studied. The concept of strong cycle is introduced and studied the properties of fuzzy end nodes and strong cycles in a fuzzy graph. Clustering techniques using distance concepts in fuzzy graphs are discussed and introduced a procedure for finding clusters of order k using distance matrix. Also clustering techniques based on the connectedness concepts in fuzzy graphs are discussed. Fuzzy graph theoretic techniques are applied in fuzzy neural network.