补图具有悬挂点且连通的图的最小特征值

The least eignvalue of the graphs whose complements are connected and have pendant vertices

图的最小特征值定义为图的邻接矩阵的最小特征值,它是刻画图的结构性质的重要参数.在给定阶数且补图为具有悬挂点的连通图的图类中,刻画了最小特征值达极小的唯一图,并给出了这类图最小特征值的下界.

The least eigenvalue of the graph is defined as the smallest eigenvalue of adjacency matrix of the graph,which is an important algebraic parameter on characterizing structural property of graphs.In this paper,we characterize the unique graph with the minimum least eigenvalue among all graphs of fixed order whose complements are connected and have pendent vertices,and present the lower bound of the least eigenvalue of such classes of graphs.