The Wiener index of a graph G, denoted W(G), is the sum distances between all non-ordered pairs vertices in G.É. Czabarka, et al. conjectured that for simple quadrangulation G on n vertices, n?4, W(G)?112n3+76n?2,n?0(mod2), 112n3+1112n?1,n?1(mod2).In this paper, we confirm conjecture.

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

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 positive integer n is said to be Wiener graphical, if there exists a graph G with Wiener index n. In this paper, we prove that any positive integer n( 6= 2, 5) is Wiener graphical. For any positive integer p, an interval [a, b] is said to be a p-Wiener interval if for each positive integer n ∈ [a, b] there exists a graph G on p vertices such that W (G) = n. For any positive integer p, an inte...

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...