A lower bound for the Laplacian eigenvalues of a graph—Proof of a conjecture by Guo Original Research Article

We show that if μj is the jth largest Laplacian eigenvalue, and dj is the jth largest degree (1less-than-or-equals, slantjless-than-or-equals, slantn) of a connected graph Γ on n vertices, then μjgreater-or-equal, slanteddj-j+2(1less-than-or-equals, slantjless-than-or-equals, slantn-1). This settles a conjecture due to Guo.