The Wiener index of a graph Gis defined as W(G) =1/2[Sum(d(i,j)] over all pair of elements of V(G), where V (G) is the set of vertices of G and d(i, j) is the distance between vertices i and j. In this paper, we give an algorithm by GAP program that can be compute the Wiener index for any graph also we compute the Wiener index of HAC5C7[p, q] and HAC5C6C7[p, q] nanotubes by this program.

Wiener index is a topological index based on distance between every pair of vertices in a graph G. It was introduced in 1947 by one of the pioneer of this area e.g, Harold Wiener. In the present paper, by using a new method introduced by klavžar we compute the Wiener and Szeged indices of some nanostar dendrimers.

Given a graph G and a set X ⊆ V (G), the relative Wiener index of X in G is defined as WX(G) = ∑ {u,v}∈(X2 ) dG(u, v) . The graphs G (of even order) in which for every partition V (G) = V1+V2 of the vertex set V (G) such that |V1| = |V2| we have WV1(G) = WV2(G) are called equal opportunity graphs. In this note we prove that a graph G of even order is an equal opportunity graph if and only if it...

Bereg and Wang defined a new class of highly balanced d-ary trees which they call k-trees; these trees have the interesting property that the internal path length and thus the Wiener index can be calculated quite easily. A k-tree is characterized by the property that all levels, except for the last k levels, are completely filled. Bereg and Wang claim that the number of k-trees is exponentially...

The Wiener index is a graph invariant that has found extensive application in chemistry. In addition to that a generating function, which was called the Wiener polynomial, who’s derivate is a q-analog of the Wiener index was defined. In an article, Sagan, Yeh and Zhang in [The Wiener Polynomial of a graph, Int. J. Quantun Chem., 60 (1996), 959969] attained what graph operations do to the Wiene...

Let $G$ be a connected graph. The Wiener index of graph is the sum distances between all unordered pairs vertices. We provide asymptotic formulae for maximum simple triangulations and quadrangulations with given connectivity, as order increases, make conjectures extremal based on computational evidence. If $\overline{\sigma}(v)$ denotes arithmetic mean from $v$ to other vertices $G$, then remot...

Given a simple connected undirected graph G, the Wiener index W (G) of G is defined as half the sum of the distances over all pairs of vertices of G. In practice, G corresponds to what is known as the molecular graph of an organic compound. We obtain a sharp lower bound for W (G) of an arbitrary graph in terms of the order, size and diameter of G.