Graphs with small second largest Laplacian eigenvalue. (English) Zbl 1284.05165
Summary: Let \(L(G)\) be the Laplacian matrix of \(G\). In this paper, we characterize all of the connected graphs with second largest Laplacian eigenvalue no more than \(l\), where \(l \dot= 3.2470\) is the largest root of the equation \(\mu^3-5\mu^2+6\mu -1=0\). Moreover, this result is used to characterize all connected graphs with second largest Laplacian eigenvalue no more than three.
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