图的谱半径的一些下界

Some Lower Bounds on the Spectral Radius of Graphs

利用矩阵的相似变换,研究了简单连通图的谱半径的可达下界,得到一个新的下界ρ（G）≥δ1＋t-s＋√（s＋t-δ1）2＋4s（δ2-t）/2,等号成立当且仅当G=~G1 G2,其中G1为n-i阶（δ1-s）-正则图,G2为i阶t-正则图。

By similar transformation of adjacent matrix, sharp lower bound of simple connective graphs spectral radius was studied. The new lower bound was gained as ρ（G）≥δ1＋t-s＋√（s＋t-δ1）2＋4s（δ2-t）/2,, which is true for equality and only when G=~G1 G2 where G1 is a （δ1-s）-regular graph of （n-i） power,G2 is a t-regular graph of power.