A new extension of the generalized topological indices (GTI) approach is carried out to represent “simple” and “composite” topological indices (TIs) in an unified way. This approach defines a GTI-space from which both simple and composite TIs represent particular subspaces. Accordingly, simple TIs such as Wiener, Balaban, Zagreb, Harary and Randić connectivity indices are expressed by means of ...

The Wiener number W (G) of a graph G is the sum of distances between all pairs of vertices of G. If (G,w) is a vertex-weighted graph, then the Wiener number W (G,w) of (G,w) is the sum, over all pairs of vertices, of products of weights of the vertices and their distance. For G being a partial binary Hamming graph, a formula is given for computing W (G,w) in terms of a binary Hamming labeling o...

Let G and H be two graphs. The corona product G o H is obtained by taking one copy of G and |V(G)| copies of H; and by joining each vertex of the i-th copy of H to the i-th vertex of G, i = 1, 2, …, |V(G)|. In this paper, we compute PI and hyper–Wiener indices of the corona product of graphs.

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 PI index is a graph invariant defined as the summation of the sums of edges of neu and nev over all the edges of connected graph G, where neu is the number of edges of G lying closer to u than to v and nev is the number of edges of G lying closer to v than to u. The index is very simple to calculate and has disseminating power similar to that of the Wiener and the Szeged indices. The compre...

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...