Graphs with small second largest Laplacian eigenvalue

Let L(G)L(G) be the Laplacian matrix of GG. In this paper, we characterize all of the connected graphs with second largest Laplacian eigenvalue no more than ll; where l≐3.2470l≐3.2470 is the largest root of the equation μ3−5μ2+6μ−1=0μ3−5μ2+6μ−1=0. Moreover, this result is used to characterize all connected graphs with second largest Laplacian eigenvalue no more than three.