仅有三个悬挂点的图的补图的最小特征值

设图G是点集为V(G)＝{v1，v2，…，vn}的简单连通图，则G的邻接矩阵是A(G)＝(aij)n×n，其中若vi和vj相邻，则aij＝1，否则aij＝0.由于A(G)是实对称的，因此可将其特征值设为λ1(G)≥λ2(G)≥…≥λn(G)，且A(G)的特征值也称为G的特征值.该文在仅有三个悬挂点的图的所有连通补图中，确定了其最小特征值达到最小值时的唯一图.

The least eigenvalue of the complements of graphs having exactly three pendent vertices

Suppose that G is a connected simple graph with the vertex set V(G)＝{v1，v2，…，vn}. Then the adjacency matrix of G is A(G)＝(aij)n×n， where aij＝1 if vi is adjacent to vj， and otherwise aij＝0. Since A(G) is real and symmetric， its eigenvalues can be arranged as λ1(G)≥λ2(G)≥…≥λn(G)， and the eigenvalues of A(G) are also called the eigenvalues of G. In this paper， the unique graph on n≥28 vertices whose least eigenvalue is minimum among the complements of all graphs having exactly three pendent vertices is determined.