wiener numbers of random pentagonal chains

Wiener numbers of random pentagonal chains

The Wiener index is the sum of distances between all pairs of vertices in a connected graph. In this paper, explicit expressions for the expected value of the Wiener index of three types of random pentagonal chains (cf. Figure 1) are obtained.

Fibonacci Numbers and the Numbers of Perfect Matchings of Square, Pentagonal, and Hexagonal Chains*

Let G be a finite graph. A perfect matching in G is a selection of edges in G such that each vertex of G belongs to exactly one selected edge. Therefore, if the number of vertices in G is odd, then there is no perfect matching. We denote by K(G) the number of perfect matchings of £, and refer to it as the K number of G. By a polygonal chain Py, s we mean a finite graph obtained by concatenating...

Hosoya polynomials of random benzenoid chains

Let $G$ be a molecular graph with vertex set $V(G)$, $d_G(u, v)$ the topological distance between vertices $u$ and $v$ in $G$. The Hosoya polynomial $H(G, x)$ of $G$ is a polynomial $sumlimits_{{u, v}subseteq V(G)}x^{d_G(u, v)}$ in variable $x$. In this paper, we obtain an explicit analytical expression for the expected value of the Hosoya polynomial of a random benzenoid chain with $n$ hexagon...

Laws of Large Numbers for Random Linear

The computational solution of large scale linear programming problems contains various difficulties. One of the difficulties is to ensure numerical stability. There is another difficulty of a different nature, namely the original data, contains errors as well. In this paper, we show that the effect of the random errors in the original data has a diminishing tendency for the optimal value as the...

Wiener and Hyper-Wiener Numbers in a Single Matrix

A novel unsymmetric square matrix, WPU , is proposed for calculating both Wiener, W , and hyper-Wiener, WW, numbers. This matrix is constructed by using single endpoint characterization of paths. Its relations with Wiener-type numbers are discussed.

On Wiener numbers of polygonal nets