Ordering Starlike Trees by the Totality of Their Spectral Moments

The k-th spectral moment Mk(G) of the adjacency matrix a graph G represents number closed walks length k in G. We study here partial order ≼ graphs, defined by H if ≤ Mk(H) for all ≥ 0, and are interested question when is linear within specified set graphs? Our main result that on each starlike trees with constant vertices. Recall connected tree it has vertex u such components − paths, called branches It turns out ordering vertices coincides shortlex sorted sequence their branch lengths.