This paper is devoted to Wiener index of directed graphs, more precisely grids. The grid Gm, n the Cartesian product Pm□Pn paths on m and vertices, in a particular case when = 2, it called ladder graph Ln. Kraner Šumenjak et al. 2021 proved that maximum digraph, which obtained by orienting edges Ln, all layers isomorphic one factor are same way except (corresponding an endvertex other factor) p...

The Wiener index of a network, introduced by the chemist Harry [30], is sum distances between all pairs nodes in network. This index, originally used chemical graph representations non-hydrogen atoms molecule, considered to be fundamental and useful network descriptor. We study problem constructing geometric networks on point sets Euclidean space that minimize index: given set P n points $$\mat...

The vertex-edge Wiener index of a simple connected graph G is defined as the sum of distances between vertices and edges of G. Two possible distances D_1(u,e|G) and D_2(u,e|G) between a vertex u and an edge e of G were considered in the literature and according to them, the corresponding vertex-edge Wiener indices W_{ve_1}(G) and W_{ve_2}(G) were introduced. In this paper, we present exact form...

In 1993 two novel distance-based topological indices were put forward. In the case of acyclic molecular graphs both are equal to the Wiener index, but both differ from it if the graphs contain cycles. One index is defined (Mohar, B.; Babić, D.; Trinajstić, N. J. Chem. Inf. Comput. Sci. 1993, 33, 153-154) in terms of eigenvalues of the Laplacian matrix, whereas the other is conceived (Klein, D. ...

In this paper, we consider a molecular descriptor called the Wiener polarity index, which is defined as the number of unordered pairs of vertices at distance three in a graph. Molecular descriptors play a fundamental role in chemistry, materials engineering, and in drug design since they can be correlated with a large number of physico-chemical properties of molecules. As the main result, we de...

The Wiener–Khintchine formula plays a central role in statistical mechanics. It is shown here that the problem of prime pairs is related to autocorrelation and hence to a Wiener–Khintchine formula. “Experimental” evidence is given for this. c © 1999 Elsevier Science B.V. All rights reserved. PACS: 05.40+j; 02.30.Nw; 02.10.Lh

Anthropogenic Biomes describe globally significant ecological patterns within the terrestrial biosphere caused by sustained direct human interaction with ecosystem, including agriculture, urbanization, forestry and other land uses. The present study focused on the invertebrate diversity in Marudhamalai Hills which is highly disturbed by human activities. Different techniques to identify the dis...