报告题目：Some extremal results on the α-spectral radius of strongly connected digraphs
报 告 人：王力工，西北工业大学，教授
报告摘要：For a given digraph $G$, let $A(G)$ and $D(G)$ denote the adjacency matrix and the diagonal matrix with outdegrees of vertices of $G$, respectively. The matrix $A_\alpha(G)$ of a digraph $G$ is defined as $A_\alpha(G)=\alpha D(G)+(1-\alpha)A(G),$ where $\alpha\in[0,1] $. The largest modulus of the eigenvalues of $A_\alpha(G)$ is called the $A_\alpha$ spectral radius of $G$, denoted by $\lambda_\alpha(G)$. In this report, we introduce some extremal results bout the spectral radius $\lambda_\alpha(G)$ of a digraph $G$ that generalize previous results about $\lambda_0(G)$ and $\lambda_{\frac{1}{2}}(G)$. We mainly characterize the extremal digraph with the maximum (or minimum) $A_\alpha$ spectral radius among all $\widetilde{\infty}$-digraphs and $\widetilde{\theta}$-digraphs on $n$ vertices. Furthermore, we determine the digraphs with the second and the third minimum $A_\alpha$ spectral radius among all strongly connected bicyclic digraphs. For $0\leq\alpha\leq\frac{1}{2}$, we also determine the digraphs with the second, the third and the fourth minimum $A_\alpha$ spectral radius among all strongly connected digraphs on $n$ vertices. Finally, we characterize the digraph with the minimum $A_\alpha$ spectral radius among all strongly connected bipartite digraphs which contain a complete bipartite subdigraph. This is a joint work with Weige Xi.
报告人简介：王力工，西北工业大学教授、博士生导师，荷兰Twente大学博士，研究方向为图论及其应用。主持国家自然基金、省、部级基金多项，作为主要成员参加国家自然科学基金多项。在《Journal of Graph Theory》、《Discrete Mathematics》、《Discrete Applied Mathematics》、《Electronic Journal of Combinatorics》、《Linear Algebra and its Applications》等国内外重要学术期刊发表学术论文200多篇。是国家级精品课程《数学建模》课程和国家级教学成果一等奖的主要参加者。曾获陕西省第九届和第十届自然科学优秀论文一等奖和二等奖各一项。曾被评为陕西省数学建模优秀指导教师和陕西省数学建模优秀组织工作者。曾被评为西北工业大学本科最满意教师。
报告时间：2023年11月23日16:00
报告地点：文渊楼B208
主办单位：伟德国际1946源自英国
