第二大特征值小于$\frac{\sqrt{5}-1}{2}$的平面图

Planar Graphs whose Second Largest Eigenvalue Smaller than $\frac{\sqrt{5}-1}{2}$

中文关键词:  平面图  第二大特征值  完全乘积

英文关键词:planar graph  the second largest eigenvalue  complete product

中文摘要:

      若能将图$G$画在一个平面上,使得任何两条边仅在顶点处相交,则称$G$是平面图.本文刻画了第二大特征值小于$\frac{\sqrt{5}-1}{2}$的所有无孤立点的平面图.

英文摘要:

      A graph $G$ is said to be planar if $G$ can be drawn on the plane in such a way that its edges intersect only at their endpoints. In this paper, all the planar graphs without isolated vertices whose second largest eigenvalue smaller than $\frac{\sqrt{5}-1}{2}$ are characterized.