New Results in Bipolar Fuzzy Graphs with an Application

Abstract

Fuzzy graph models take on the presence being ubiquitous in environmental and fabricated structures by humans, specifically the vibrant processes in physical, biological, and social systems. Owing to the unpredictable and indiscriminate data which are intrinsic in real life, problems are often ambiguous, so it is very challenging for an expert to exemplify those problems by applying a fuzzy graph. Bipolar fuzzy graphs, belonging to the fuzzy graphs family have good capabilities when facing problems that cannot be expressed by fuzzy graphs. Therefore, in this paper, we have introduced the degree and total degree of an edge in the cartesian product of two bipolar fuzzy graphs. Likewise, μ −complement, self μ −complement, and self weak μ −complement on bipolar fuzzy graphs have been presented. Finally, an application of bipolar fuzzy digraphs in social relations has been given.