New Concepts of Bipolar Fuzzy Graphs
Abolfazl Lakdashti, Hossein Rashmanlou, R. A. Borzooei, S. Samanta and M. Pal
The energy of a graph is the sum of the absolute values of its eigenvalues. It is used in chemistry to approximate the total π-electron energy of molecules. In this paper, the concept of energy of fuzzy graph is extended to the energy of bipolar fuzzy graph. It has many applications in computer science, physics, chemistry, and other sciences. We define adjacency matrix, degree matrix, laplacian matrix, spectrum, and energy of a bipolar fuzzy graph in terms of their adjacency matrix. Also, the lower and upper bounds for the energy of a bipolar fuzzy graph are also derived.
Keywords: Bipolar fuzzy set, spectrum, energy of bipolar fuzzy graph