给定控制数为2的图的谱半径的下界

A Lower Bound on Spectral Radius of Graphs with Given Domination Number 2

一个图G(V,E)的控制数γ(G)是V的这样一个子集S的最小基数,使得G中每一个顶点或者在S中或者和S中的一些顶点邻接。本文讨论了控制数为2的n阶简单连通图的邻接谱半径下界,给出了谱半径达到最小时的极图。

The domination number γ（G） of a graph G（V,E） is the minimum cardinality of a subset S of V such that every vertex is either in the set S or is adjacent to some vertices in the set.In this paper we study a lower bound on spectral radius of graphs on n vertices with domination number 2,and determine the extremal graphs that attain the lower bound on spectral radius.