Sharp bounds for Laplacian spectral moments of digraphs with a fixed dichromatic number

The k-th Laplacian spectral moment of a digraph G is defined as Eni=1 lambda ki, where lambda i are the eigenvalues of the Laplacian matrix of G and k is a nonnegative integer. For k = 2, this invariant is better known as the Laplacian energy of G. We extend recently published results by characterizing the digraphs which attain the minimal and maximal Laplacian energy within classes of digraphs with a fixed dichromatic number. We also determine sharp bounds for the third Laplacian spectral moment within the special subclass which we define as join digraphs. We leave the full characterization of the extremal digraphs for k >= 3 as an open problem.(c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).