极大外平面图谱半径的上界

The Upper Bound of Spectral Radius of Certain Maximal Outer Great Plane

每个点都在图的一个面的边界上的平面图叫外平面图,具有最大边数的外平面图叫极大外平面图.首先给出了一类极大外平面图的特征多项式的表达式,由此给出了对任意n≥4都成立的极大外平面图谱半径的一个上界,并证明了当图的点数增大时,这个上界与谱半径是等价的无穷大量.

A graph is outerplanar if it can be embedded in the plane such that all vertices lie on the outrace boundary.The number of the edge of an outer plane graph is maximum that is called maximal outerplanar graph.In the paper,we have given characteristic polynomial of certain outerplanar graph.Thus we have obtained the upper bound of spectral radius of maximal outerplanar graph for n ≥4.We prove the upper bound is the equivalent infinite large of the spectral radius when the number of vertices of certain outerpla-nar graphs increases.