Determining sets and resolving sets of coprime graphs

报告题目：Determining sets and resolving sets of coprime graphs

报告人：郭秀云（上海大学教授，博士生导师）

报告时间：5月22日上午9:00-10:00

腾讯会议号：694-210-317

Abstract.Let Γ = (V,E) be a graph with vertex set V and edge set E, and let Aut(Γ) be the group of automorphisms of Γ. Recall that a subset D of the vertex set V of a graph Γ is called a determining set if every automorphism of Γ is uniquely determined by its action on the vertices of D. The minimum size of determining set is a measure of graph symmetry and the sets themselves are useful in studying problems involving graph automorphisms. A subset R of the vertex set V of a graph Γ is called a resolving set (or locating set) if every vertex in Γ is uniquely determined by its distances from the vertices of R. Determining (resolving) sets are said to have the exchange property in Γ if whenever S and R are minimal determining (resolving) sets for Γ and r ∈ R, then there exists s ∈ S so that (S \{s})∪{r} is also a minimal determining (resolving) set. In this talk we will introduce our work for a set becoming a determining set or a resolving set in a coprime graph, and then we show that minimal determining sets of coprime graphs satisfy the exchange property and minimal resolving sets of coprime graphs does not satisfy the exchange property.

  简 历：郭秀云上海大学数学系二级教授，博士生导师，香港中文大学获博士学位。应邀科研合作的著名大学有：澳大利亚国立大学, 西班牙巴伦西亚大学、美国俄亥俄州立大学、西班牙巴伦西亚工业大学、香港中文大学、德国Friedrch－Schiller大学和Justus-Liebig大学等学校。多年来一直从事有限群论的研究，主要集中在有限群的饱和群系、相关正规补、幂自同构、子群格、以及子群的拓扑结构等方面。承担国家自然科学基金6项、教育部博士点基金、上海市浦江人才基金、白玉兰人才基金、以及上海市自然科学基金等。曾获省部级科技进步一等奖、二等奖、自然科学三等奖各一项、以及国务院政府特殊津贴等