Kemeny's constant is a meaningful index of the communicability in a network, which combines the long-term and short-term behavior of related Markov chains. Lorenzo Ciardo et al. provided an expression for Kemeny's constant of a tree obtained by concatenating some given rooted trees. In this paper, by extending some results of the expression, we provide sharp upper and lower bounds on Kemeny's constant of trees with fixed order n and matching number β. All the corresp...
