图的一些性质的补图谱充分条件

Spectral Conditions for Some Special Graphical Properties

图的邻接矩阵的最大特征值被定义为谱半径,对于非负整数k,若连续连接图G中度和不小于k的不相邻点对,直到没有这样的点对存在后,所得到的图称为图G的k-闭包,记作cl_(k)(G)。图的谱半径和闭包运算是分析图的结构性质的重要概念。本文首先根据稳定性进行闭包运算,再利用补图的谱半径提出了给定大的最小度的图包含C_(s),P_(s),K_(2,s),sK_(2)或s-因子的充分条件。这为我们研究图的某些性质提供了一种极好的思路。

The maximum eigenvalue of the adjacency matrix for a graph is defined as the spectral radius.For nonnegative integer,the-closureof a simple graphof orderis the graph obtained fromby not recursively joining pairs of nonadjacent vertices with degree-sum at leastuntil no such pairs of vertices existing.The spectral radius of a graph and closure operation are important concepts on analyzing structural properties for a graph.In this paper,we first begin with the closure operation according to the stability and then present the sufficient conditions for a graph with large minimum degree to contain aor-factor in terms of spectral radius of its complement,which provides an idea to study some properties for a graph.