有限图的测地线传递性

数学理论与应用 ›› 2021, Vol. 41 ›› Issue (4): 32-.

有限图的测地线传递性

靳伟¹ 谭利²

1. 中南大学数学与统计学院, 长沙, 410075； 2. 江西财经大学统计学院, 南昌, 330013

出版日期:2021-12-30 发布日期:2021-12-22

On the Geodesic-transitivity of Finite Graphs

1. School of Mathematics and Statistics, Central South University, Changsha 410075, China; 2. School of Statistics, Jiangxi University of Finance and Economics, Nanchang 330013, China

Online:2021-12-30 Published:2021-12-22
Contact: Jin Wei(1982−),PhD；E−mail：jinweipei82@163.com
Supported by:
This work was supported by the NNSF of China (12061034,12071484), NSF of Jiangxi (20192ACBL21007, GJJ190273) and CPSF(2019T120563)

摘要/Abstract

摘要： 在过去几十年中人们对有限图的对称性进行了大量的研究. 本论文主要是讨论一类特殊的图对称性--(局部) $s$-测地线传递性. 最近几年来, 图的(局部) $s$-测地线传递性得到了大量的研究也取得了丰富的研究结果, 很多比较重要的基础问题得到了解决或部分解决, 同时也提出了很多新的问题. 在本领域的研究中, 所用到的研究工具和方法主要是深刻的群论知识, 包括有限单群的分类定理,也要用到组合数学领域的各种研究技巧.

关键词: 凯莱图； , $s$-测地线传递图； , 置换群

Abstract:

The symmetry problem for finite graphs has been extensively investigated over the past

few decades. This article is devoted to giving an introduction in one particular family of symmetric

graphs, namely (locally) $s$-geodesic-transitive graphs. Recently, substantial progress has been made on the study of this family of graphs, many

open problems have been solved, and many new research problems have arisen.

The methods used in this area range

from deep group theory, including the finite simple group classification, through to combinatorial

techniques.

Key words: Cayley graph; , $s$-geodesic-transitive graph; , , Permutation group

靳伟谭利. 有限图的测地线传递性[J]. 数学理论与应用, 2021, 41(4): 32-.