The Wiener index, W , is the sum of distances between all pairs of vertices in a graph G. The quadratic line graph is defined as L(L(G)), where L(G) is the line graph of G. A generalized star S is a tree consisting of ∆ ≥ 3 paths with the unique common endvertex. A relation between the Wiener index of S and of its quadratic graph is presented. It is shown that generalized stars having the prope...

Let G be a graph. Denote by L(G) its i-iterated line graph and denote by W (G) its Wiener index. There is a conjecture which claims that there exists no nontrivial tree T and i ≥ 3, such that W (L(T )) = W (T ), see [5]. We prove this conjecture for trees which are not homeomorphic to the claw K1,3 and the graph of letter H.

A simpliied way of deriving of realizable and explicit Wiener lters is presented. Discrete time problems are discussed, in a polynomial equation framework. Optimal lters, predictors and smoothers are calculated by means of spectral factorizations and linear polynomial equations. A new tool for obtaining these equations, for a given problem structure, is described. It is based on evaluation of o...

Let G be a molecular graph. The Wiener index of G is defined as the summation of all distances between vertices of G. In this paper, an exact formula for the Wiener index of a new type of nanostar dendrimer is given.

The Wiener Index, or the Wiener Number, also known as the “sum of distances” of a connected graph, is one of the quantities associated with a molecular graph that correlates nicely to physical and chemical properties, and has been studied in depth. An index proposed by Schultz is shown to be related to the Wiener Index for trees, and Ivan Gutman proposed a modification of the Schultz index with...

The intercorrelation between a series of physicochemical parameters and topological indices for a set of beta-blockers is investigated. Partition coefficients are calculated using the ClogP program, and the results are compared with previous data, both experimental and theoretical. These data are complemented by hydrophilicity and solubility calculations, together with the determination of mole...

let g be a simple connected graph. the generalized polarity wiener index ofg is defined as the number of unordered pairs of vertices of g whosedistance is k. some formulas are obtained for computing the generalizedpolarity wiener index of the cartesian product and the tensor product ofgraphs in this article.

The sum of distances between all pairs of vertices W (G) in a connected graph G as a graph invariant was first introduced by Wiener [9] in 1947. He observed a correlation between boiling points of paraffins and this invariant, which has later become known as Wiener index of a graph. Today, the Wiener index is one of the most widely used descriptors in chemical graph theory. Due to its strong co...

the edge versions of reverse wiener indices were introduced by mahmiani et al. veryrecently. in this paper, we find their relation with ordinary (vertex) wiener index in somegraphs. also, we compute them for trees and tuc4c8(s) naotubes.