Abstract
The Randić index of a graph G is defined as R ( G ) = ∑ u ∼ 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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