关于五个顶点不存在不对称的简单图  

Simple Graphs about Five Vertices without Asymmetry

作　　者：魏新杨 

机构地区：[1]辽宁师范大学数学学院,辽宁 大连

出　　处：《应用数学进展》2025年第3期220-228,共9页Advances in Applied Mathematics

摘　　要：本文讨论五个顶点不存在不对称的简单图,基于对最小度δ进行讨论的基础上,从两个顶点是否相邻以及是否有公共邻居这个角度出发,利用反证法以及给出每种情况的具体画法,进而得出结论。近百年来,国内外很多学者都对这一问题进行了研究。由于涉及的画法较多且证明过程较为复杂,国内外关于此领域的研究进展缓慢。相比较而言,本文从特殊的视角出发使得问题较为轻松得到解决,更具创新性。This paper discusses the simple graph of five vertices without asymmetry, based on the discussion of the minimum degree, from the point of view of whether the two vertices are adjacent and whether there are common neighbors, the conclusion is drawn by using the counter-evidence method and the specific drawing method of each case. In the past hundred years, many scholars at home and abroad have studied this problem. Due to the many drawings involved and the complexity of the proof process, the progress of domestic and foreign research in this field has been slow. In contrast, this paper makes the problem easier to be solved from a special perspective, which is more innovative.

关 键 词：图论 简单图 公共邻居 

分 类 号：O157.5[理学—数学]