The Wiener index of a graph G is defined to be 2 , ( ) ( , ), u V G d u ∈ ∑ X X where d(u, X) is the distance between the vertices u and X in G. In this paper, we obtain an explicit expression for the Wiener index of an odd graph.

The Wiener index, defined as the total sum of distances in a graph, is one of the most popular graph-theoretical indices. Its average value has been determined for several classes of trees, giving an asymptotics of the form Kn5/2 for some K. In this note, it is shown how the method can be extended to trees with restricted degrees. Particular emphasis is placed on chemical trees – trees with max...

Let O be a hyper-positive set. The goal of the present article is to examine hulls. We show that Shannon’s criterion applies. It is essential to consider that R̃ may be Wiener. Recent interest in matrices has centered on extending integral triangles.

Abstract The n-th order Wiener index of a molecular graph G was put forward by Estrada et al. [New J. Chem. 22 (1998) 819] as ( ) 1 ( , ) n n x W H G x where ( , ) H G x is the Hosoya polynomial. Recently Brückler et al. [Chem. Phys. Lett. 503 (2011) 336] considered a related graph invariant, ( ) 1 1 (1/ !) ( ( , )) / n n n n x W n d x H G x d x . For n=1, both W and W reduce to the ordinary W...

the padmakar-ivan (pi) index is a first-generation topological index (ti) based on sums overall edges between numbers of edges closer to one endpoint and numbers of edges closer to theother endpoint. edges at equal distances from the two endpoints are ignored. an analogousdefinition is valid for the wiener index w, with the difference that sums are replaced byproducts. a few other tis are discu...

The Wiener index W is the sum of distances between all pairs of vertices of a (connected) graph. Hexagonal systems (HS’s) are a special type of plane graphs in which all faces are bounded by hexagons. These provide a graph representation of benzenoid hydrocarbons and thus find applications in chemistry. The paper outlines the results known for W of the HS: method for computation of W , expressi...

Let $G$ be a finite group. The intersection graph of is whose vertex set the all proper non-trivial subgroups and two distinct vertices $H$ $K$ are adjacent if only $H\cap K \neq \{e\}$, where $e$ identity group $G$. In this paper, we investigate some properties exploring topological indices such as Wiener, Hyper-Wiener, first second Zagreb, Schultz, Gutman eccentric connectivity $D_{2n}$ for $...

Abstract This work presents a simple method for partitioning the bond‐additive and atoms‐pair‐additive distance‐based topological indices of plane graphs into sum contributions inner faces. The proposed is applied to decompose several (Wiener, hyper‐Wiener, Tratch‐Stankevich‐Zefirov, Balaban, Szeged indices) ring series benzenoid systems. It was found that employed scheme providing an accurate ...