2023/05/10 by Xiuwen Yang, Hajo Broersma, Yang, Xiuwen +3
Chemistry · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Spectral Theory in Mathematical Physics #Synthesis and Properties of Aromatic Compounds
paper · pdf · doi:10.48550/arxiv.2305.06362
openalex publication_date 2023/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
The k-th Laplacian spectral moment of a digraph G is defined as ∑i=1n λik, where λi 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.