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...

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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.

Let G be a simple connected graph. The generalized polarity Wiener index of G is defined as the number of unordered pairs of vertices of G whose distance is k. Some formulas are obtained for computing the generalized polarity Wiener index of the Cartesian product and the tensor product of graphs in this article.

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.

The sum of distances between all the pairs of vertices in a connected graph is known as the {it Wiener index} of the graph. In this paper, we obtain the Wiener index of edge complements of stars, complete subgraphs and cycles in $K_n$.

Using a non-uniformly distributed aperture radar system for forming a SAR image will result in data correlations between the SAR image resolution cells. Thus, this requires that a more robust filter than the Matched Filter, i.e. the MMSE or Wiener Filter to be used in the receiver processing. As the Wiener Filter involves a computationally expensive matrix inverse operation, it can be avoided b...

The nonlinear speech signal decomposition based on Volterra-Wiener functional series is described. The solution of speech recognition problem by means of measuring Wiener kernels is proposed. The recognition system of speech signal is considered for speech phoneme identification.

Network structures are everywhere, including but not limited to applications in biological, physical and social sciences, information technology, and optimization. Network robustness is of crucial importance in all such applications. Research on this topic relies on finding a suitable measure and use this measure to quantify network robustness. A number of distance-based graph invariants, also ...

This paper deals with the study of the Malliavin calculus of Euclidean motions on Wiener space, (i.e. transformations induced by general measure preserving transformations, called 'rotations', and H-valued shifts) and the associated flows on abstract Wiener spaces.