If G is a tree, then L(G)D(G)L(G)=-2L(G). Is the opposite true?

It is well known that if graph G is a tree, then the following identity holds: LDL=-2L, where L is the Laplacian matrix of tree G, and D is its distance matrix. Is the opposite true? That is, if...

29 May 2020 4,434 3 View