Lexicographical ordering by spectral moments of trees with a given bipartition

Abstract

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.