The Wiener index has been studied for simply generated random trees, non-plane unlabeled random trees and a huge subclass of random grid trees containing random binary search trees, random medianof-(2k+ 1) search trees, random m-ary search trees, random quadtrees, random simplex trees, etc. An important class of random grid trees for which the Wiener index was not studied so far are random digi...

The Wiener index is a graphical invariant that has found extensive application in chemistry. We define a generating function, which we call the Wiener polynomial, whose derivative is a q-analog of the Wiener index. We study some of the elementary properties of this polynomial and compute it for some common graphs. We then find a formula for the Wiener polynomial of a dendrimer, a certain highly...

Network structures are everywhere, including but not limited to applications in biological, physical and social sciences, information technology, and optimization. Network robustness is of crucial importance in all such applications. Research on this topic relies on finding a suitable measure and use this measure to quantify network robustness. A number of distance-based graph invariants, also ...

the wiener index w(g) of a connected graph g is defined as the sum of the distances betweenall unordered pairs of vertices of g. the eccentricity of a vertex v in g is the distance to avertex farthest from v. in this paper we obtain the wiener index of a graph in terms ofeccentricities. further we extend these results to the self-centered graphs.

Complex networks are ubiquitous in biological, physical and social sciences. Network robustness research aims at finding a measure to quantify network robustness. A number of Wiener type indices have recently been incorporated as distance-based descriptors of complex networks. Wiener type indices are known to depend both on the network's number of nodes and topology. The Wiener polarity index i...

The reverse Wiener index of a connected graph G is defined as Λ(G) = 1 2 n(n− 1)d−W (G), where n is the number of vertices, d is the diameter, and W (G) is the Wiener index (the sum of distances between all unordered pairs of vertices) of G. We determine the n-vertex non-starlike trees with the first four largest reverse Wiener indices for n > 8, and the nvertex non-starlike non-caterpillar tre...