On the conjecture of Delorme, Favaron and Rautenbach about the Randic index [An article from: European Journal of Operational Research]

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Description:
Let G(k,n) be the set of connected graphs without multiple edges or loops which have n vertices and the minimum degree of vertices is k. The Randic index @g=@g(G) of a graph G is defined by: @g=@?"("u"v")(@d"u@d"v)^-^1^/^2, where @d"u is the degree of vertex u and the summation extends over all edges (uv) of G. In this paper we prove the conjecture of Delorme, Favaron and Rautenbach about the graphs for which the Randic index attains its minimum value when k=n2. We show that the extremal graphs must have n-k vertices of degree k and k vertices of degree n-1.