Let χ(G

x)be the characteristic polynomial of G.In this paper we establish the follow Theorem 1.Let G and (?) be two disjoint nontivial connected simple graphs. The graph G(u)1 is obtained from G by connecting new edge fromo u to a new vertex.The graph (?)(u

v)(?) is obtain by connecting the vertices u and v of G and (?)respectively to a new edge.If χ(G(v)1

x)ρ(G(v')1)

Them we have χ(G(v

u)(?)

x)ρ(G(v'

u)(?)) and ρ(G(v

u)(?)>ρ(G(v'

u)(?)) Using thes theorem we extent seme result in[2]and Consider the largest eigenvalue of some condensed cycle connected with other graphs.