Balance spherical fuzzy graph and their applications

Abstract

Spherical fuzzy graphs (SFGs) can be considered an advancement beyond the original idea of picture fuzzy graphs (PFGs). The balanced spherical fuzzy graph constitutes a distinct category within the realm of spherical fuzzy graphs. We propose the idea of balanced spherical fuzzy graphs based on density functions in this study and look into some of its characteristics. This article explores the essential and comprehensive criteria required to determine balanced spherical fuzzy graphs. Additionally we have developed an approach to evaluate the spherical fuzzy graph (SFGs) is balanced or not. In summary, this article provides an exemplification of how the utilization of balanced spherical fuzzy graphs (SFGs) can effectively portray the interconnections among neighboring nations.