当前位置: X-MOL 学术Math. Proc. Camb. Philos. Soc. › 论文详情
On the Saxl graph of a permutation group
Mathematical Proceedings of the Cambridge Philosophical Society ( IF 0.737 ) Pub Date : 2018-08-08 , DOI: 10.1017/s0305004118000610
TIMOTHY C. BURNESS; MICHAEL GIUDICI

Let G be a permutation group on a set Ω. A subset of Ω is a base for G if its pointwise stabiliser in G is trivial. In this paper we introduce and study an associated graph Σ(G), which we call the Saxl graph of G. The vertices of Σ(G) are the points of Ω, and two vertices are adjacent if they form a base for G. This graph encodes some interesting properties of the permutation group. We investigate the connectivity of Σ(G) for a finite transitive group G, as well as its diameter, Hamiltonicity, clique and independence numbers, and we present several open problems. For instance, we conjecture that if G is a primitive group with a base of size 2, then the diameter of Σ(G) is at most 2. Using a probabilistic approach, we establish the conjecture for some families of almost simple groups. For example, the conjecture holds when G = Sn or An (with n > 12) and the point stabiliser of G is a primitive subgroup. In contrast, we can construct imprimitive groups whose Saxl graph is disconnected with arbitrarily many connected components, or connected with arbitrarily large diameter.
更新日期:2020-02-11

 

全部期刊列表>>
化学/材料学中国作者研究精选
Springer Nature 2019高下载量文章和章节
《科学报告》最新环境科学研究
ACS材料视界
自然科研论文编辑服务
中南大学国家杰青杨华明
剑桥大学-
中国科学院大学化学科学学院
材料化学和生物传感方向博士后招聘
课题组网站
X-MOL
北京大学分子工程苏南研究院
华东师范大学分子机器及功能材料
中山大学化学工程与技术学院
试剂库存
天合科研
down
wechat
bug