Some classification of graphs in fuzzy labeling

Abstract

This research amplify the strength of the fuzzy labelling approach for analysing fuzzy graceful labelling of graphs have been proved for the graphs like complete bipartite graph, flower graph and bow graph, fuzzy vertex graceful labelling with some results have been proved for wheel graph and fan graph. Fuzzy edge-vertex graceful labelling have been examined on star graph and helm graph and an analytical research on super graceful path and tree graphs with the labelling which belongs to [0,1] are also analysed in detail. Some special graphs such as path graph, butterfly graph and tree graph are connected with fuzzy antimagic graph and cycle graph, friendship graph,wheel graph, gear graph, prism graph, barbell graph, flower graph, ladder graph, fan graph and some cycle related graphs are connected with fuzzy antimagic labelling and proved with antimagic conditions. Fuzzy graceful labelling of antimagic graphs have been proved for path graph and butterfly graph. newline