A note on the third invariant factor of the Laplacian matrix of a graph
Abstract
Let G be a simple connected graph with n≥ 5 vertices. In this note, we will prove that s3(G)≤ n, and characterize the graphs which satisfy that s3(G)=n, n-1, n-2, or n-3, where s3(G) is the third invariant factor of the Laplacian matrix of G.
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