Lexicographical ordering by spectral moments of trees with 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 < k < n .