A Study on Energy of Fuzzy Graphs and its Applications

Abstract

This research amplify the energy of graphs approach for analysing energy of fuzzy Labelling of graphs have been proved for the graphs like complete graph, flower graph and wheel graphs. Energy of fuzzy graceful Labelling of graphs have been proved for the graphs like bipartite graph, friendship graph, planar graph. Some special Labelling graphs such as path graph, butterfly graph and tree graph are connected with energy of fuzzy antimagic graph and cycle graph. Energy of fuzzy graceful Labelling of antimagic graphs have been proved for path graph and butterfly graph. A graph is a representation of relationships between objects. If two objects (called vertices)are related, then there is an edge between them and the vertices are adjacent. An example of a large graph is the internet, where web pages are the vertices and links between them are the edges. Graph theory employs a variety of techniques to explore the properties of graphs, borrowing from algebra, analysis, combinatorics, probability theory, and others. newline