Extremal Estrada indices of the weighted trees with fixed total weight sum

摘要

Let T(n,m) be the set of positively weighted trees of order n with the fixed total weight sum m, where all the weights are integers and m≥n−1≥3. Among T(n,m), the weighted trees with the maximal and the second maximal Estrada indices are derived for m≥n−1≥3 and m≥n+1≥7, respectively.