A Study Of Odd Graceful Labeling Of Cycles With Two Parallel Chords

Graph theory is an important branch of discrete mathematics.The main content of this paper is about the labeling problem of graphs.A.Rosa has proposed the famous graceful tree conjecture,and then people began to focus on and research the labeling problem of graphs.Subsequently,some conclusions on labeling graphs have been applied in physics,chemistry,geography,astronomy and so on,especially computer.In recent years,graph labeling has rapidly developed from nothing,and its theory has gradually improved,so that people began to study some new labeling graphs and methods.The articles about labeled graphs are increasing everyday,including graceful labeling,harmonious labeling and friendly labeling which are the most popular in the research.Gnanajoth defined the odd graceful labeling and proved many related graphs.Previously,researchers have researched the odd graceful labeling about the circle graph and the dragon graph.In this paper,we combine the label characteristics of the previous circle graph,and prove the odd graceful labeling of circle graphs by constructing a reasonable labeling method.The thesis combined the labeling characteristics of previous circle graphs with the odd gracefulness of circle graphs containing two parallel chords.The details are following:1.Odd graceful labeling of circle graphs with adjacent chords and symmetry circle;2.Odd graceful labeling of circle graphs with adjacent chords and asymmetric circle;3.Odd graceful labeling of circle graphs with nonadjacent chords and symmetry circle;4.Odd graceful labeling of circle graphs with nonadjacent chords and asymmetric circle.By research the characteristics and the rules of the labeling,the general theoretical problem can be resolved,that is,odd graceful labeling of cycles with two parallel chords.Moreover,according to odd graceful labeling of simple graphs,more general rules can be found,and the corresponding odd graceful labeling can be conformed,illustrating the accuracy of labeling by the corresponding proof and examples.