(n,m)中谱半径最小的图的一个特征

CHARACTIRIZATION OF THE GRAPH WITH THE SMALLEST SPECTRAL RADIUS IN *V (n,m)/

设（ｎ，ｍ）表示具有ｎ个顶点ｍ条边的有限简单连通图，ρ（Ｇ）是Ｇ的最大特征值，也称为Ｇ的谱半径。若Ｇ∈（ｎ，ｍ），ｍ≥ｎ＋１，且ρ（Ｇ）＝ｍｉｎ｛ρ（Ｈ）：Ｈ∈（ｎ，ｍ）｝，则Ｇ一定不含悬挂边。

Let (n,m) be the simple connected graphes with n vertices and m edges, ρ(G) denotes the largest eigenvalue of the graph G . The following result is obtained.If G ∈ ( n,m),m≥n+1 and ρ(G)= min {ρ(H):H∈ (n,m)}, then G does not contain pendant edge.