文摘
Let λ2(G)λ2(G) be the second smallest normalized Laplacian eigenvalue of a graph GG. In this paper, we determine all trees with λ2(T)≥1−32. Meanwhile, if TT is a tree of diameter 66, then we prove that λ2(T)≤1−32. Moreover, we determine all trees of diameter d=3d=3 or 66 with λ2(T)=1−32.