On a Conjecture about the Randić Index and Diameter
نویسندگان
چکیده
The Randić index of a graph G is defined as R(G) = ∑ u∼v (d(u)d(v))− 2 , where d(u) is the degree of vertex u, and the summation goes over all pairs of adjacent vertices u, v. A conjecture of R(G) for connected graph with n vertices is as follows: R(G)−D √2− n+1 2 and R(G) D 1 2 + √ 2−1 n−1 , where D is the diameter of G. In this paper, we prove that this conjecture is true for unicyclic graphs.
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