报告题目：Some extremal results related to a poset of

trees

主讲人：李书超（华中师范大学数学与统计学院）

            报告邀请人：孙怡东教授

            会议时间： 2021年4月6日 15:30-17:00

            点击链接直接加入会议：https://meeting.tencent.com/s/25AVOfwu6Mc5

            会议 ID： 382 374 512

            报告摘要：In this talk, we give an extensive study on the Wiener indices, the number of closed walks, the coefficients of some graph polynomials (the adjacency polynomial, the Laplacian polynomial, the edge cover polynomial and the independence polynomial) of trees. Csikvari (2010) introduced the generalized tree shift, which keeps the number of vertices of trees. Applying the generalized tree shifts and recurrence relation, we extend the works of Csikvari [Combinatorica, 30 (2010) 125-137; J. Graph Theory 74 (2013) 81-103]. Using a unified approach, we obtain the following main results: Firstly, for all n and l, we characterize the unique tree having the maximum (resp. minimum) Wiener index and the unique tree having the maximum (resp. minimum) number of closed walks of length l among the trees of order n which are neither a path nor a star. Secondly, we characterize the unique tree whose adjacency polynomial (resp. Laplacian polynomial, independence polynomial) has the maximum (resp. minimum) coefficients in absolute value among the trees of order n which are neither a path nor a star, respectively. At last, we identify all the n -vertex trees whose edge cover polynomial has the minimum coefficients in absolute value and we also determine the unique tree having the maximum coefficients in absolute value among the trees of order n which are neither a path nor a star.

         个人简介：李书超，理学博士，教授，博士生导师，主要从事组合数学、图论及其应用方面的研究。相继在Advances in Applied Mathematics, Journal of Algebraic Combinatorics, European Journal of Combinatorics, Journal of Combinatorial Designs, Discrete Mathematics等20余个重要国际学术期刊发表论文100余篇。先后主持完成国家自然科学基金项目3项，科技部项目2项。2013年入选教育部“新世纪优秀人才支持计划”。主持完成的课题“图的几类不变量的研究”获湖北省自然科学奖。目前是中国运筹学会理事、中国运筹学会图论组合分会理事、湖北省运筹学会常务理事、美国《数学评论》评论员、德国《数学评论》评论员。