Some recent results on independence polynomials of graphs


报告题目: Some recent results on independence polynomials of graphs


报告人:Prof. Bing WeiUniversity of Mississippi






摘要:An independent set of a graph $G$ is a set of pairwise non-adjacent vertices. Let $\alpha(G)$ denote the cardinality of a maximum independent set and $f_s(G)$ for $0\le s\le \alpha(G)$ denote the number of independent sets of $s$ vertices. The independence polynomial $I(G;x)=\sum_{i=0}^{\alpha(G)}f_s(G)x^s$ defined first by Gutman and Harary has been the focus of considerable research recently. In this talk, we will first introduce some basic concepts and tools related to the indepence polynomials of graphs, and then present some bounds for $f_s(G)$ when $G$ is a $k$-tree, a maximum  $k$-degenerate graph or a compound graph. Additionally, we will characterize  graphs which attain our  bounds. Finally, we  will propose several further research problems.


报告人简介: 主要从事有关图的结构性理论,图的参数以及极图理论等方面的研究工作。在对图的圈,路和因子的结构,图的控制数,图的独立多项式等问题的研究中,获得一些深刻的结果。在国内工作期间,曾获得博士后基金,多项国家自然科学基金,留学回国人员基金,香港裘槎基金等项目的资助。曾经担任中国运筹学会副秘书长,中国图论学会秘书长。曾任中科院研究员,博士生导师。目前已发表论文七十余篇,许多论文被国内外学者多次引用。为多个国际或国内杂志审稿。应邀在国际或国内多个学术研究机构从事合作研究。多次在国际或国内学术会议上作邀请报告。




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