连通图的谱半径上界

Bounds of the Spectral Radius of Connected Graphs

图谱理论是图论研究的重要的领域之一.设图G是n阶简单连通图,具有n顶点和m条边的连通图,p(G)为图G的邻接矩阵的谱半径.利用代数的方法得出两个ρ(G)的上界为:■与■和达到上界的图.

The theory of graph spectrum is an important area in graph theory.LetGbe a simple connected with n vertices,m edges andρ（G）be the adjacency spectral radius of G. In this paper,by using algebraic techniques,this paper presents the upper bound ofρ（G）：ρ（u）≤√2m＋tv/mv（δ-1）-（n-1）δ and ρ≤√vmv the extreme graphs arriving the bound.