Balance Spherical Interval Valued Fuzzy Graphs

Abstract

Spherical interval-valued fuzzy graphs (SIvFGs) represent a further advancement of the original concept of spherical fuzzy graphs (SFGs). Within this framework, the balanced spherical fuzzy graph forms a distinct subclass that highlights equilibrium in structural relationships. In this study, we introduce the concept of balanced spherical interval-valued fuzzy graphs based on density functions and investigate their fundamental properties and examine their key properties. We also establish a set of comprehensive criteria for determining whether a given SIvFG is balanced. Furthermore, an analytical approach is developed to determine whether an SIvFG is balanced. Overall, this work illustrates how balanced spherical interval-valued fuzzy graphs can effectively model and interpret the interconnections among neighboring nations.