A New Graphical Representation of the Old Algebraic Structure

The most recent advancements in algebra and graph theory enable us to ask a straightforward question: what practical use does this graph connected with a mathematical system have in the real world? With the use of algebraic approaches, we may now tackle a wide range of graph theory-related problems. We compute loop-involutions and nonself-loop-involutions of flexible weak inverse property loops. Importantly, diameter, radius, and eccentricity of this loop structure’s inverse graph have all been calculated in a broad manner. Some topological indices, as an application of inverse graph, are also given at the end of the paper.