科研动态

数学与统计及交叉学科前沿论坛------高端学术讲座第39场

讲座题目:Inverses of bicyclic graphs with a unique perfect matching

主讲人:魏二玲

讲座时间:2021.11.12(周五)14:00-15:00

讲座地点:腾讯会议690 515 624

主讲人简介:

魏二玲,中国人民大学副教授,硕士生导师,民进中国人民大学专家委员会委员。研究方向:图论与组合优化、图神经网络。毕业于北京交通大学,主持和参加国家自然科学基金多项。

主讲内容:

Let $G$ be a graph. The inverse of $G$ is a weighted graph $(G^{-1}, w)$ such that $V(G^{-1})=V(G)$ and $[w(ij)]_{n\times n}=A(G)^{-1}$ for each pair of vertices $i$ and $j$ of $G$, where $A(G)$ is the adjacency matrix of $G$. A weighted graph $(G,w)$ with weight function $w: E(G)\to \{-1,0,1\}$ is called a signed graph or a mixed graph. A perfect matching of a graph $G$ is a set of disjoint edges which cover all vertices of $G$. A simple connected graph $G$ of order $n$ is bicyclic if it has $n+1$ edges.Let $\mathcal B$ be the family of all bicyclic graphs with a unique perfect matching. In this paper, we show that every graph $G$ in $\mathcal{B}$ is invertible and its the inverse is bipartite if and only if $G$ is bipartite. Further, we characterize all graphs in $\mathcal{B}$ which have a signed graph as its inverse.