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

Tomas Vetrik, Mesfin Masre, Selvaraj Balachandran


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.


zeroth-order general Randić index; tree; distance k-domination number

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