SOME RESULTS ON BIPOLAR FUZZY SELF CENTERED GRAPHS

Abstract

The distance and related concepts like eccentricity, radius, diameter, center, periphery, etc. are already defined and used in many applications of graph theory. In this paper, we define a new distance called bipolar fuzzy distance in bipolar fuzzy graphs. Using this distance, we define the concepts of  bipolar fuzzy eccentricity, bipolar fuzzy center, etc. and  establish the relation between bipolar fuzzy radius and bipolar fuzzy diameter. Also the concept of self centered graphs is generalized to bipolar fuzzy self centered graphs and a necessary condition for a bipolar fuzzy graph to be a bipolar fuzzy self centered graph is obtained. The max-max and min-min composition of the bipolar fuzzy distance matrix is introduced, and we also present an easy check to see whether a given bipolar fuzzy graph is bipolar fuzzy self centered or not.