Zeroth-order general Randić index of trees with given distance k-domination number

Abstract

The zeroth-order general Randić index of a graph G is defined as R a ( G )=∑ v ∈ V ( G ) d G a ( v ) , where a ∈ ℝ , V ( G ) is the vertex set of G and d G ( v ) is the degree of a vertex v in G . We obtain bounds on the zeroth-order general Randić index for trees of given order and distance k -domination number, where k ≥ 1 . Lower bounds are given for 0 < a < 1 and upper bounds are given for a < 0 and a > 1 . All the extremal graphs are presented which means that our bounds are the best possible.