On Modified and Reverse Wiener Indices of Trees
نویسندگان
چکیده
two sides of the edge e, and where the summation goes over all edges of T . The λ -modified Wiener index is defined as Wλ (T ) = ∑ e [nT,1(e) · nT,2(e)] . For each λ > 0 and each integer d with 3 ≤ d ≤ n− 2, we determine the trees with minimal λ -modified Wiener indices in the class of trees with n vertices and diameter d. The reverse Wiener index of a tree T with n vertices is defined as Λ (T) = 2 n(n−1)d(T )−W (T ), where d(T ) is the diameter of T . We prove that the reverse Wiener index satisfies the basic requirement for being a branching index.
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