Study On Odd Graceful Labelings Of Star And Cycle Combination Graphs

Since the labeling problem was introduced by Rosa A in the 1960 s,it has attracted the attention of many scholars.Then some conclusions on the labeling graph theory are using in many fields,such as coding theory,data base,information science and technology,economics and so on.People gradually improve the theory of graph labelings and begin to study some new labeling and labeling methods.For decades,a short period of time,the labeling graph has experienced and rapid development,there have thousands of articles about labeling graph,among them,the graceful labelings,harmonious labelings and friendly labelings are more.In 1991,Gnanajoth defined the odd graceful labelings and proved many odd graceful graphs,then more people focused their attentions on the graph which combined by basic graphs.The combination graphs refers to some basic graphs by cartesian product,with or without intersection union,a point connect or an edge coincidence to combine a new graph,the combination endless.Before this people,the scholars have studied the union graph of two similar or different class graph,this paper will study the odd graceful labeling of star(s)and circle(s)on the basis of the previous graphs.Specific research is divided into four parts:1.Odd graceful labeling of a star and a circle;2.Odd graceful labeling of a number of stars and a circle;3.Odd graceful labeling of a star and a number of cycles;4.Odd graceful labeling of a number of stars and many circles.By summarizing the characteristic and the rule of the labeling,we provide an odd graceful labeling for constructing and give the proof and examples to illustrate the accuracy of the labelings.The last part of this paper will introduce a new combination graph of star and circles.By summarizing the connection characteristic to find out an odd graceful labeling which conform to the objective law,and give corresponding proofs and examples to illustrate the accuracy of the labelings.