Zeroth-order general Randić index of trees with given distance k-domination number - Tomas Vetrik; Mesfin Masre; Selvaraj Balachandran (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2022)
The zeroth-order general Randić index of a graph G is defined as Ra(G)=∑v ∈ V(G)dGa(v), where a ∈ ℝ, V(G) is the vertex set of G and dG(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.