It is well known that the algebraic connectivity of a graph is the second small eigenvalue of its Laplacian matrix. In this paper, we mainly research the relationships between the algebraic connectivity and the disjoint vertex subsets of graphs, which are presented through some upper bounds on algebraic connectivity.

中文翻译：

---

图的代数连通性和不相交顶点子集

众所周知，图的代数连通性是其拉普拉斯矩阵的第二个小特征值。在本文中，我们主要研究代数连通性与图的不相交顶点子集之间的关系，这些关系通过代数连通性的一些上限给出。