In 1994, Dobrynin and Kochetova introduced the concept of degree distance DD(Γ) a connected graph Γ. Let dΓ(S) be Steiner k-distance S⊆V(Γ). The Wiener k-index or k-center indexSWk(Γ) Γ is defined by SWk(Γ)=∑|S|=kS⊆V(Γ)dΓ(S). distanceSDDk(Γ) SDDk(Γ)=∑|S|=kS⊆V(Γ)∑v∈SdegΓ(v)dΓ(S), where degΓ(v) vertex v in this paper, we consider Nordhaus–Gaddum-type results for SWk(Γ) SDDk(Γ). Upper bounds on SW...

The eccentricity of a vertex $v$ is the maximum distance between $v$ and anyother vertex. A vertex with maximum eccentricity is called a peripheral vertex.The peripheral Wiener index $ PW(G)$ of a graph $G$ is defined as the sum ofthe distances between all pairs of peripheral vertices of $G.$ In this paper, weinitiate the study of the peripheral Wiener index and we investigate its basicproperti...

in this paper, a novel topological index, named m-index, is introduced based on expanded form of the wiener matrix. for constructing this index the atomic characteristics and the interaction of the vertices in a molecule are taken into account. the usefulness of the m-index is demonstrated by several qspr/qsar models for different physico-chemical properties and biological activities of a large...

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...