Enumeration of Laplacian integral and {-1,0,1}-diagonalizable graphs

Nathaniel Johnston, Sarah Plosker, Luis M. B. Varona

A graph with Laplacian matrix $L$ is called Laplacian integral if the eigenvalues of $L$ are all integers, and it is called $\{-1,0,1\}$-diagonalizable if $L$ has a full set of eig…