On majorization of closed walk vectors of trees with given degree sequences

摘要

Let C-v(k; T) be the number of closed walks of length k starting at vertex v in a tree T. We prove that for any tree T with a given degree sequence Tr, the vector C(k; T) (C-v(k; T), v is an element of V (T)) is weakly majorized by the vector C(k; T-pi*) (C-v(k, T-pi*), v is an element of V (T-pi*)), where T-pi* is the greedy tree with the degree sequence pi. In addition, for two trees degree sequences pi' and pi, if Tr is majorized by pi', then C(k; T-pi*) is weakly majorized by C(k; T-pi*). (C) 2018 Elsevier Inc. All rights reserved.