关于处处可断图类的最大谱半径

On the Maximum Spectral Radius of the Class of Everywhere Separable Graphs

以复杂网络研究为背景,讨论了处处可断图类在复杂网络分析中的应用.通过研究处处可断图类的性质,刻画了该类图的一些基本拓扑结构,研究了处处可断图类的代数结构.利用图的顶点划分方法,证明了当谱半径达到最大时该图类的极图,并给出了该图类谱半径的一个上界.

Based on the research of complex networks, the applications of the class of everywhere separable graphs were discussed. Through the investigation on the properties of this class of graphs, some fundamental topological structures of this class of graphs were obtained. The algebraic structures of this class of graphs were researched. Making use of the method of vertex partitioning of graphs, the extrereal graph is attained as the spectral radius of everywhere separable graphs reach to its maximum. An upper bound of the maximum spectral radius is found.