On the Randic Image index

  title={On the Randic Image index},
  author={Charles Delorme and Odile Favaron and Dieter Rautenbach},
  journal={Discrete Mathematics},
The Randi c index R(G) of a graph G = (V; E) is the sum of (d(u)d(v))−1=2 over all edges uv∈E of G. Bollob as and Erdős (Ars Combin. 50 (1998) 225) proved that the Randi c index of a graph of order n without isolated vertices is at least √ n− 1. They asked for the minimum value of R(G) for graphs G with given minimum degree (G). We answer their question for (G) = 2 and propose a related conjecture. Furthermore, we prove a best-possible lower bound on the Randi c index of a triangle-free graph G… CONTINUE READING

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