Novel Concepts in Bipolar Fuzzy Graphs with Applications

Abstract

Many problems of practical interest can be modeled and solved by using bipolar graph algorithms. Bipolar fuzzy graph (BFG), belonging to fuzzy graphs (FGs) family, has good capabilities when facing with problems that cannot be expressed by FGs. Hence, in this paper, we introduce the notion of ϑ,δ−homomorphism of BFGs and classify homomorphisms (HMs), weak isomorphisms (WIs), and co-weak isomorphisms (CWIs) of BFGs by ϑ,δ−HMs. Also, an application of homomorphism of BFGs has been presented by using coloring-FG. Universities are very important organizations whose existence is directly related to the general health of the society. Since the management in each department of the university is very important, therefore, we have tried to determine the most effective person in a university based on the performance of its staff.