Bounding The Zeroth-order Randic Index Of Trees With A Given Size Of The Maximum Matchings

This paper studies the extremal problem related to zeroth-order Randic index of trees with a given size of the maximum matchings. The main results are as follows:(1). Whenα= -1 , the maximum value and minimum value of 0Rαare determined and, furthermore, the corresponding extremal trees are also characterized.(2). When 0 <α< 1, the maximum value of ~0R_αand the corresponding extremal trees are determined;(3). When -1 <α< 0, the minimum value of ~0R_αand the corresponding extremal trees are determined.