Undergraduate thesis opening report

2. The main research contents of the thesis: the cayley diagram of the group and the existence of the hamilton circle and the path, mainly to summarize and summarize some special and commonly used groups.

3. Significance of the topic: 1. Concretize the highly abstract group into a visible model corresponding to the structure of the group. 2. This paper establishes a connection between two modern important disciplines, "group theory" and "graph theory". This article also allows us to further understand and review some of the "old friends" of the group - the cyclic group, the two-sided group, the direct product of the group, the generator and its operation relationship. 4. More importantly, to study the problem It will make you feel interesting.

4. The key problem of solving: summarizing and summarizing the graph representation of some special groups and the existence of hamilton circle and path, trying to prove the familiar theorem from the graph and introduce some results. For hamilton The existence of the hamilton circle in the hamilton path and cayley,, }:q4+zm), and the existence of the hamilton circle in the graph cayley,,}: q8+zm). Summarize that there are two generators. The undirected cayley diagram and its related properties, especially the existence of the cayley diagram of s6 and its hamilton circle.

5. Theoretical basis and research innovation: In this paper, the concept of group cayley diagram is introduced and some common groups are studied and summarized. The cayley diagram of the research group will make us have a visual understanding of the abstract group. Observing the excellent properties of some special group cayley graphs. Studying this problem can not only further understand and review the cyclic group, the dihedral group, the direct product of the group, the generator and its operation relationship, but also feel very interesting.

The research innovation is to express some cayley diagrams of special groups, and observe the relationship between groups and groups through graphs, and prove and generalize the existence of some special groups of hamilton circles and paths. For example, hamilton group, q4 +zm, q8+zm, the cayley diagram of s6 and the existence of its hamilton circle.

6, test literature directory

1 Jiang Changhao, Graph Theory and Network Flow, Beijing, China Forestry Press, XX.7

2 i.grossman w.magnus, groups and their graphs

3 igor pak and rados radoicic, hamilton paths in cayley graphs

7. Overall arrangement and specific progress of the work

At the beginning of February - at the end of February, I will give a study to my teacher.

At the beginning of March - in mid-March, check the relevant information

The paper will be finalized in late March and will be finalized.

The first draft was finalized in early April and revised and corrected under the guidance of Teacher Lin.

The paper was completed in early May.