2022-04-26 信息来源：腾讯会议
举办单位：数学科学学院
负责人：林上为
电话：13835184047
活动主题：characterizations on graphs which achieve some upper bounds for their zero forcing number
形式：学术报告
活动内容摘要：let $g$ be a connected graph of order $n$ with vertex set $v(g)$. a set $s\subseteq v(g)$ is a zero forcing set of $g$ if initially the vertices in $s$ are colored black and the remaining vertices are colored white, and then forcing a white vertex to black if it is the only white neighbor of some black vertex, applying this step iteratively until all vertices of $g$ are black. the zero forcing number $z(g)$ of $g$ is defined as the minimum cardinality of a zero forcing set of $g$. in a recent work [theory appl. graphs 2(2) (2015) article 2] caro and pepper used a greedy algorithm to prove that $z(g)\leq \frac{(\delta-2)n-(\delta-\delta) 2}{\delta-1}$, where $\delta$, $\delta\geq 2$ are minimum degree, maximum degree of $g$, respectively. if $g$ is regular, i.e., $\delta=\delta$, this upper bound was characterized independently by gentner et al. and lu et al. in 2016. first, we completely characterize general graphs attained the upper bound, solving the question proposed by lu et al. on the other hand, $z(g)\leq n-g 2$, where $g$ is the girth of $g$. second, we slightly improved the bound and characterize connected graphs attained the improved bound.
主讲人基本情况：徐守军，兰州大学数学与统计学院教授、副院长、博士生导师。2007年获得兰州大学博士学位。2008-2010年中科院数学与系统科学研究院从事运筹学方向博士后工作；多次到美国加州大学戴维斯分校计算机系和香港教育学院访问。研究兴趣主要在图论及组合最优化、计算机算法及离散数学等。在siam j discrete math、discrete appl. math、j. combin. optim.、australas. j. combin.等杂志上发表多篇学术论文，目前主持一项国家面上基金。
听众范围：数学科学学院师生
举办时间：2022年4月30日
举办地点：腾讯会议（581-512-864）
报告类型：理科类