The Randic index of a graph G is defined as R(G) = Sigma(u similar to v)(d(u)d(v))(-1/2), where d(u) is the degree of vertex u and the summation goes over all pairs of adjacent vertices u, v. A conjecture on R(G) for connected graph G is as follows: R(G) >=? r(G)-1, where r(G) denotes the radius of G. We proved that the conjecture is true for biregular graphs, connected graphs with order n <= 10 and tricyclic graphs.
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