Research And Analysis On The Sequence Of Two Classes Of Graphs Structured By Circle

Graph labeling problem as a classical problem, occupies an important position in thegraph theory. A graph labeling is a mapping that has been founded between the vertex set andinterger set. This mapping educes another mapping from the edge set to integer set for a graph,and this mapping accords with some requirements. At present, the research results aboutgraph labeling has been widely used in astronomy, physics, biology, computer science andother fields.This thesis selects a branch of graph labeling problems-the sequential labeling as themain research content. The sequential labeling was presented by Chang, Hsu and Grace in1980, when they solving the problem of error correcting code in computer code by theharmonious labeling of the graph, which is a class of graph labeling has been derived by theharmonious labeling.This thesis introduces the origin and development of graph theory and simply introducesthe presence of graceful labeling, harmonious labeling and sequential labeling, summarizesthe research and development status of this several classes of graph labeling. At the same time,this thesis discusses some properties of the sequential graph and introduces several sufficient,necessary, sufficient and necessary conditions about the sequential graph. these theoriesprovide the theoretical basis for identifying a class of graph with a sequential labeling andconstructing a sequential graph. And these theories give the theoretical supporting to theresearch of this thesis.The sequence of two classes graph structured by the disjoint circle has been researchedin this thesis. As the basis of the above theories, the sequential labeling method of odd circleis improved, the conclusion of minimum edge labeling is applied in made beginning label onodd circle and made labeling for other vertices according to the characteristics of sequentiallabeling.At the same time, considering the disjoint of circle structure and value of general graph,the value k in graph is divided into k4m, k4m1, k4m2, k4m3four kinds ofsituations according to mod4, then further argument will be divided into four kinds ofcircumstances according to the value of m and the graph labeling situation, It obtained thesequential labeling of two different graphC9C2kandC11C2k, and gives the strictmathematical proof.