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

Tomas Vetrik (Department of Mathematics and Applied Mathematics, University of the Free State, Bloemfontein, South Africa)
Mesfin Masre
Selvaraj Balachandran

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 10, No 1 (2022): Electronic Journal of Graph Theory and Applications

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.