含有割点的图的最小特征值

On the Least Eigenvalue of Graphs with Cut Vertices

中文关键词:  邻接矩阵  最小特征值  最小图  割点.

英文关键词:adjacency matrix  least eigenvalue  minimizing graph  cut vertex.

中文摘要:

      设${\mathscr S}$为某些图构成的集合. 若在集${\mathscr S}$中图$G$的最小特征值达到最小, 则称$G$为该图集的最小图. 本文确定了集${\mathscr G}_n$的最小图, 其中${\mathscr G}_n$为含有割点的$n$阶连通图构成的集合.

英文摘要:

      Let ${\mathscr{S}}$ be a certain set of graphs. A graph is called a minimizing graph in the set ${\mathscr{S}}$ if its least eigenvalue attains the minimum among all graphs in ${\mathscr{S}}$. In this paper, we determine the unique minimizing graph in ${\mathscr {G}}_n$, where ${\mathscr {G}}_n$ denotes the set of connected graphs of order $n$ with cut vertices.