非正则k-连通图的谱半径

The Spectral Radius of Non-regular k-connected Graph

一个图G被说成是k-连通的,如果它的点连通度大于等于k.对正则k-连通图,谱半径等于最大度,而对非正则k-连通图,其谱半径严格小于最大度,研究此时最大度与谱半径差值的下界是图谱理论中一个很有意义的问题.通过研究图的结构,利用著名的柯西—施瓦兹不等式,给出了上述差值的一个精确的下界.

For a regular k -connected graph G ,p （G） = A , but for non-regular k -connected graph G ,p （G） 〈 A , hence the investigation on the lower bound of the difference A-p（G） is a very interesting topic in spectra graph theory. This paper investigates the structure of graph and provides a lower bound of A-p（G） by using the Cauthy-Sehwarz Inequality.