报告名称：Traversibility of subspace based nonzero component graph of vector spaces over finite fields

报告专家：周国飞

专家所在单位：南京大学

报告时间：2022年4月24日16：00-18：00

报告地点:腾讯会议（会议号：536756642）

专家简介：周国飞，南京大学数学系教授, 1990-1994年就读于浙江师范大学数学系，获学士学位，1994-1999就读于南京大学，获理学博士学位，2005年-2006年在美国密歇根州立大学做访问学者。研究领域涉及有向图的圈, 图的染色,超图的度序列, Ramsey理论等. 主持与参与多项自然科学基金, 曾在European J. of Combinatorics, Discrete Math., Graphs and Combinatorics 等杂志上发表论文多篇. 

报告摘要：Let $\mathbb{V}$ be an$n$-dimensional vector space over a field $\mathcal{F}$ having basis $\mathcal{B}=\left\lbrace \alpha_1, \alpha_2, \dots, \alpha_n\right\rbrace $ and $W$ be an $m$ dimensional subspace of $\mathbb{V}$ with basis $\{\alpha_{w_1}, \alpha_{w_2},\dots, \alpha_{w_m}\}$, where $\alpha_{w_i}$ is some $\alpha_{j}\in \mathcal{B}$. The $subspace~based~nonzero~component~graph$, denoted by $\Gamma_W(\mathbb{V}_\alpha)=\left( V,E\right)$, of a finite dimensional vector space with respect to $W$ and $\mathcal{B}$ is defined as follows: $V=\mathbb{V}\setminus W$ and for $\mathbf{u},\mathbf{v}\in V$, there is an edge between $\mathbf{u}$ and $\mathbf{v}$ if and only if either $W_{\mathbf{u}}\subset W_{\mathbf{v}}$ or $W_{\mathbf{v}}\subset W_{\mathbf{w}}$, where $\mathbf{u}=u_1\alpha_1+u_2\alpha_2+\dots+u_k\alpha_k$, $1\leq k\leq n$ and $W_{\mathbf{u}}=\{\alpha_{w_1}, \alpha_{w_2},\dots, \alpha_{w_m}\}\cup \{\alpha_1, \alpha_2, \dots, \alpha_k\}$. In this paper, we determine the order, size and edge-connectivity of $\Gamma_W(\mathbb{V}_\alpha)$. We show that the graph $\Gamma_W(\mathbb{V}_\alpha)$ is Hamiltonian but not Eulerian. We also show that under some mild conditions, the graph $\Gamma_W(\mathbb{V}_\alpha)$ is triangulated. Finally, we determine the clique number and the chromatic number of $\Gamma_W(\mathbb{V}_\alpha)$.