ENERGY AND LAPLACIAN ENERGY ON INVERSE FUZZY GRAPH

Real-time problems involving uncertain or indeterminate information can be effectively addressed using fuzzy graphs (FGs). However, the problems in which the edge membership values have a significant impact due to the combination of its corresponding vertices remain unsolved. To address this, inverse fuzzy graph (IFG) was introduced.

In this article, the energy ($E^{I}$) and the Laplacian energy ($LE$) on inverse fuzzy graph (IFG) $G^{I}$ have been newly introduced. Further, various lower and upper bounds are derived for $E^{I}(G^{I})$ and $LE(G^{I})$. Additionally the sharp bound is estimated for $E^{I}(G^{I})$ which aids in determining the minimum and maximum bounds for $E^{I}(G^{I})$. Furthermore, for the newly defined $l-$ regular IFG, the equality condition $E^{I}(G^{I})=LE(G^{I})$ holds true.