Distance in Fuzzy Graphs: g-distance, µ -distance, d- distance, and ss-distance

This work mainly focuses on different distance concepts in fuzzy graphs. The properties of δ- 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.

Dr.Sameena Kalathodi is Assistant Professor,Mathematics Department,M.E.S Mampad College,University of Calicut.Completed Ph.D from NIT Calicut.Several papers published in international journals.Awarded Women scientist fellowship(2009)by Department of Science and technology,India.Interested Area: Fuzzy Mathematics, Graph Theory,Applied Mathematics.