Palindromic complexity of trees

We consider finite trees with edges labeled by letters on a finite alphabet $\varSigma$. Each pair of nodes defines a unique labeled path whose trace is a word of the free monoid $\varSigma^*$. The set of all such words defines the language of the tree. In this paper, we investigate the palindromic complexity of trees and provide hints for an upper bound on the number of distinct palindromes in the language of a tree.