Comparative results between the number of subtrees and Wiener index of graphs

For a graph G , we denote by N ( ) the number of non-empty subtrees . If is connected, its Wiener index W sum distances between all unordered pairs vertices In this paper establish some comparative results and It shown that > if order n ≥ 7 diameter 2 or 3. Also graphs are constructed with large diameters Moreover, for tree T ≇ S prove starlike maximum degree 3 exactly two degrees one which has leaf neighbors, broom k log leaves. And method provided constructing < Finally several related open problems proposed to comparison