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The general Randić index Rα(G) of a graph G is defined by Rα(G)=∑uv(d(u)d(v))α, where d(u) is the degree of a vertex u, and the summation extends over all edges uv of G. Some results on trees with a given order and matching number that have minimum general Randić index have been obtained. However, the corresponding maximum problem has not been studied, and usually the maximum problem is much harder...
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