Cyclic Symmetry of Riemann Tensor in Fuzzy Graph Theory

Abstract

In this paper, we define a graph-theoretic analog for the Riemann tensor and analyze properties of the cyclic symmetry. We have developed a fuzzy graph-theoretic analog of the Riemann tensor and have analyzed its properties. We have also shown how the fuzzy analog satisfies the properties of the 6X6 matrix of the Riemann tensor by expressing it as a union of the fuzzy complete graph formed by the permuting vertex set and a Levi-Civita graph analog. We have concluded the paper with a brief discussion on the similarities between the properties of the fuzzy graphical analog and the Riemann tensor and how it can be a plausible analogous model for the Petrov-Penrose classification.