图的谱半径和泛圈性

Spectral Radius and Pancyclicity of a Graph

设G=(V,E)是一个n阶m条边的简单连通图,μ(G)为图的邻接矩阵的最大特征值。本文利用图的谱条件讨论了图的泛圈性,证明了n(n≥5)阶图G,如果μ(G)>n-2,则G是泛圈图除非G=Kn-1+e。

Let G=（V,E） be a simple connected graph with n vertices and m edges and μ（G） be the largest eigenvalue of its adjacency matrix.In this paper,we study pancyclic graph via spectral conditions,and show that if G is a graph of order n（n≥5） with μ（G）n-2,then G is a pancyclic graph unless G=Kn-1＋e.