Sharp bounds on the zeroth-order general Randić index of trees in terms of domination number

<abstract><p>The zeroth-order general Randić index of graph $ G = (V_G, E_G) $, denoted by ^0R_{\alpha}(G) is the sum items (d_{v})^{\alpha} over all vertices v\in V_G where \alpha a pertinently chosen real number. In this paper, we obtain sharp upper and lower bounds on ^0R_{\alpha} trees with given domination number \gamma for \alpha\in(-\infty, 0)\cup(1, \infty) \alpha\in(0, 1) respectively. The corresponding extremal graphs these are also characterized.</p></abstract>