Sharp bounds for the Randić index of graphs with given minimum and maximum

@inproceedings{Suil2017SharpBF,
  title={Sharp bounds for the Randi{\'c} index of graphs with given minimum and maximum},
  author={Suil and Yongtang Shi},
  year={2017}
}
The Randić index of a graph G, written R(G), is the sum of 1 √ d(u)d(v) over all edges uv in E(G). Let d and D be positive integers d < D. In this paper, we prove that if G is a graph with minimum degree d and maximum degree D, then R(G) ≥ √ dD d+Dn; equality holds only when G is an n-vertex (d,D)-biregular. Furthermore, we show that if G is an n-vertex… CONTINUE READING