Lexicographical ordering by spectral moments of trees with k pendant vertices and integer partitions

Lexicographic ordering by spectral moments (S-order) among all trees is discussed in this paper. For integers n and k, let p(n,k) be the number of all partitions of n into k parts. The last p(n−1,k) graphs, in the S-order, among all trees with n vertices and k pendant vertices are determined for 2