Survey on the general Randić index: extremal results and bounds

Abstract

For α∈ℝ, the general Randić index of a graph G is defined as Rα(G)=∑uv∈E(G)[d(u)d(v)]α, where E(G) is the edge set of G, and d(u) and d(v) are the degrees of vertices u and v in G, respectively. We give a survey containing known extremal results about the general Randić index. We present results for general graphs, trees, unicyclic graphs, bicyclic graphs and chemical graphs.