The Wiener matrix and the hyper-Wiener number of a tree (acyclic structure), higher Wiener numbers of a tree that can be represented by a Wiener number sequence W, W,W.... whereW = W is the Wiener index, and R W k K    ,.... 2 , 1 is the hyper-Wiener number. The concepts of the Wiener vector and hyper-Wiener vector of a graph are introduced for the molecular graph of bi-phenylene. Moreover, ...

The edge versions of reverse Wiener indices were introduced by Mahmiani et al. very recently. In this paper, we find their relation with ordinary (vertex) Wiener index in some graphs. Also, we compute them for trees and TUC4C8(s) naotubes.

let g be a simple graph. the hosoya polynomial of g is ( , ) ,( , ) = { , } ( ) xd u v h g x  u v v gwhere d(u,v) denotes the distance between vertices u and v . the dendrimer nanostar is apart of a new group of macromolecules. in this paper we compute the hosoya polynomial foran infinite family of dendrimer nanostar. as a consequence we obtain the wiener index andthe hyper-wiener index of th...

In theoretical chemistry, -modified Wiener index is a graph invariant topological index to analyze the chemical properties of molecular structure. In this note, we determine the minimum -modified Wiener index of graph with fixed connectivity or edge-connectivity. Our results also present the sufficient and necessary condition for reaching the lower bound.

The Wiener index of a connected graph G, denoted by W (G), is defined as 12 ∑ u,v∈V (G) dG(u, v). Similarly, the hyper-Wiener index of a connected graph G, denoted by WW (G), is defined as 1 2W (G) + 1 4 ∑ u,v∈V (G) dG(u, v). The vertex Padmakar-Ivan (vertex PI) index of a graph G is the sum over all edges uv of G of the number of vertices which are not equidistant from u and v. In this paper, ...

In this paper, the concepts of Wiener index of a vertex weighted and edge weighted graphs are discussed. Vertex weight and edge weight of a clique are introduced. Wiener index of a vertex weighted partial cube is also discussed. Also a new concept known as Connectivity index is introduced. A relation between Connectivity index and Wiener index for different graphs are discussed.

Polynomial interpolation can be used to obtain closed formulas for topological indices of infinite series of molecular graphs. The method is discussed and its advantages and limitations are pointed out. This is illustrated on fullerenes C12k+4 and four topological indices: the Wiener index, the edge Wiener index, the eccentric connectivity index, and the reverse Wiener index. The results for th...