Extremal trees for the Randić index with given domination number

摘要

The Randić index is the topological index most widely used in applications for chemistry and pharmacology. It is defined for a graph G with vertex set V(G) and edge set E(G) asR(G)=∑uv∈E(G)1deg(u)deg(v),where deg(u) and deg(v) denote the degrees of the vertices u, v ∈ V(G). In this paper we find upper and lower bounds of the Randić index of trees in terms of the order and the domination number. The extremal trees are characterized.