The Study Of The Graph Model And It’s Label Number Based On The Bipartiality Of The Label

The label problem of a graph originates from the famous graceful tree association of A.Rosa in 1966.A vertex mark of a graph is the mapping of the vertex set of the graph to the integer set,while the edge mark is the mapping of the edge set of the graph to the integer set.In this paper,a special network model is given—the definition and properties of the lantern graph and the combined complete bipartite graph,and a new labeling,odd-edge magic labeling is put forward.In addition,the labeling method for the special network model of the class is given.It is also proved that the special network model of this kind is an odd edge magic graph.Through the experiment,we also get,the conclusion that the special network model satisfies the graceful graph and the odd-even edge double labeling.Further,the relationship between odd-edge magic labeling,set-ordered graceful labeling and set-ordered odd-graceful labeling are studied.