on the skew spectral moments of trees with a given bipartition

Let g be a simple graph, and g be an oriented graph of g with an orientation and skew-adjacency matrix s(g). let λ1(g), λ2(g), . . . , λn(g) be the eigenvalues of s(g). the number n i=1 λk(g) (k = 0, 1, . . . , n − 1), denoted by tk(g), is called the k-th skew spectral moment of g, and t (g) = (t0(g), t1(g), . . . , tn−1(g)) is the sequence of skew spectral moments of g. suppose g1 and g2 are two digraphs. we shall write g1 ≺t g2 (g1 comes before g2 in a t -order) if for some k (1 ≤ k ≤ n−1), ti(g1) = ti(g2) (i = 0, 1, . . . , k−1) and tk(g1) < tk(g2) hold. for two given positive integers p and q with p ≤ q, we denote t p,q = {t : t is a tree of order n with a (p, q)-bipartition }. in this paper, we discuss t -order among all trees in t p,q. furthermore, the last three trees, in the t -order, underlying graphs among t p,q (4 ≤ p ≤ q) are characterized.