单圈图的第二个特征值的下确界

Sharp Lower Bound of the Second Largest Eigenvalue of a Unicyclic Graph

设Ｇ为ｎ阶连通单圈图，λ２（Ｇ）为Ｇ的第二个特征值．文中的主要结果如下：当ｎ≥８时，λ２（Ｇ）≥λ２（Ｓ），且等号成立的充要条件是Ｇ≌Ｓ；当ＧＳ且ｎ≥８时，λ２（Ｇ）≥１．

Let λ2(G) be the second largest eigenvalue of a unicyclic connectedgraph G.Our main results are:(1)λ2,(G)≥λ2(S) with equality iff G≌S￣3 in the case of n ≥8.(2) If G S and n ≥8,then λ2(G) ≥1.