Analytical study of various dominations on bipolar fuzzy graphs

Abstract

In this paper we discussed the prominence of Bipolar fuzzy graphs (BFG). Fuzzy set assigns a sequence of membership values to the elements of the universal set ranging from 0 to 1, whereas now our study about Bipolar fuzzy graphs whose membership degree range is [-1, 1]. The earnest efforts of the researchers are perceivable in the relevant establishment of the subject integrating coherent practicality and reality. When we assess the position of an object in space, we may have positive information expressed as a set of possible places and negative information expressed as a set of impossible places. This corresponds to the idea that the union of positive and negative information does not cover the whole space. Dominating sets have a vital function regarding the theory of fuzzy graphs. Traveling salesman problem, communication network, traffic route problem are largely discussed applications among the diverse applications dealing with the theory of dominations. In this paper we generalized Bipolar fuzzy graphs and explored various types of dominations on Bipolar fuzzy graphs such as Strong Dominations, Split and non-split dominations, Multiple dominations and some applications of Bipolar fuzzy graphs. Fuzzy graphs found an increasing number of applications in modeling real time systems where the information inherent in the system varies with different levels of precision. Bipolar fuzzy graphs can be used to model many problems in economics, operations research, etc; involving two similar, but opposite type of qualitative variables like success and failure, gain and loss etc.