LAPLACIAN SPECTRUM OF FUZZY CYCLE

Abstract Laplacian spectrum plays a vivacious part in the field of sciences. Multiplicities of integer eigenvalues and spectral effects of various modifications for Laplacian spectrum of simple graphs has been conferred [1]. But, Laplacian spectrum of fuzzy graphs, because of its complexity in calculation, is a barrier in utilizing the concept in various fields. When the fuzzy graph is larger there arise a grim in calculation part. Minor error at any point will disturb the spectrum of Laplacian drastically. Our idea is to overcome the exertion and make it unpretentious by finding the Laplacian spectrum of any fuzzy graph directly from its edge membership value or vertex membership value. Thoroughly analyzing various types of fuzzy graphs for its characteristics, contour and comportment of its Laplacian Spectrum and explored some interesting outcomes. In this study, we focused on fuzzy cycle and vertex regular fuzzy cycle for its structure, pattern of labelling so as to deduce its least and greatest eigenvalues of its corresponding Laplacian matrix as well as their behavior by using only the edge membership value of the given graph. This study approaches the least and greatest eigen values of Laplacian matrix for a fuzzy cycle directly from its edge membership value itself.