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 graph G is equal to the sum of distances between all pairs of vertices of G, It is known that the Wiener index of a molecular graph correlates with certain physical and chemical properties of a molecule. In the mathematical literature, many good algorithms can be found to eompute the distances m a graph, and these can easily be adapted for the caleulation of the Wiener ind...

Motivated by the terminal Wiener index‎, ‎we define the Ashwini index $mathcal{A}$ of trees as‎ begin{eqnarray*}‎ % ‎nonumber to remove numbering (before each equation)‎ ‎mathcal{A}(T) &=& sumlimits_{1leq i

A variational representation for positive functionals of a Hilbert space valued Wiener process (W (·)) is proved. This representation is then used to prove a large deviations principle for the family {G (W (·))} >0 where G is an appropriate family of measurable maps from the Wiener space to some Polish space.

let g be a connected simple (molecular) graph. the distance d(u, v) between two vertices u and v of g is equal to the length of a shortest path that connects u and v. in this paper we compute some distance based topological indices of h-phenylenic nanotorus. at first we obtain an exactformula for the wiener index. as application we calculate the schultz index and modified schultz index of this ...

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...

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.