lexicographic ordering by spectral moments ($s$-order) among all trees is discussed in this
paper. for two given positive integers $p$ and $q$ with $pleqslant q$, we denote $mathscr{t}_n^{p, q}={t: t$ is a tree of order $n$ with a $(p, q)$-bipartition}. furthermore, the last four trees, in the $s$-order, among $mathscr{t}_n^{p, q},(4leqslant pleqslant q)$ are characterized.