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)...

Complex networks abound in physical, biological and social sciences. Quantifying a network's topological structure facilitates network exploration and analysis, and network comparison, clustering and classification. A number of Wiener type indices have recently been incorporated as distance-based descriptors of complex networks, such as the R package QuACN. Wiener type indices are known to depe...

The Wiener index of a strong digraph D is defined as the sum shortest path distances between all ordered pairs vertices. This definition has been extended to digraphs that are not necessarily by defining distance from vertex b 0 if there no in D. Knor et al. (2016) [9] considered (not strong) orientations graphs with maximum index. authors conjectured for given tree T, an orientation T always c...