报告题目：On the number of spanning trees with a perfect matching of a class of split graphs

报告人：周金秋（集美大学 博士）

报告时间：2025年8月18日（星期一） 下午16:30-17:00

地点：明理楼426

报告摘要： A spanning tree of a simple graph $G$ is a \textit{matchable spanning tree} if it has a perfect matching of $G$. Let $t'(G):=|\{T: T \mbox{ is a matchable spanning tree of }G\}|$. In 1984, Simion first investigated the enumerative problem concerning matchable spanning trees in the complete graph $K_{2n}$ and proved that $t'(K_{2n})=(2n)^{n-2}(2n)!/n!$. Let $G\vee G'$ be the join of two vertex-disjoint graphs $G$ and $G'$. The paper obtains that $t'(G\vee K_n^c)=(n-1)!\prod_{i=1}^{n-1}(2n+\mu_i(G))$ if $|V(G)|=n$, where $\{\mu_1(G)\geq \mu_2(G)\geq \cdots\geq \mu_{n-1}(G)\geq \mu_{n}(G)=0\}$ is the Laplacian spectrum of $G$, and $K_n^c$ the complement of $K_n$. Moreover, we prove that $t'(K_r\vee K_s^c)=2\times r!(r+s)^{(r-s-2)/2}(2r+s)^{s-1}/[(r-s)/2]!$ if $r\geq s$ and $r\equiv s~(mod~2)$.

报告人简介：

周金秋，女，集美大学在读博士。主要从事图的生成树和完美匹配的计数及其在统计物理中的应用等方面的研究工作。近几年在包括Discrete Applied Mathematics和Graph and Combinatorics等多种国际SCI检索的期刊上发表论文6篇。