Forests are biologically diverse systems, representing some of the richest biological areas on Earth. They offer a variety of habitats for plants, animals and micro-organisms. However, forest biodiversity is increasingly threatened as a result of deforestation, fragmentation, climate change and other stressors. Biodiversity is the variation of life forms within a given ecosystem, biome, or on t...

Forests are biologically diverse systems, representing some of the richest biological areas on Earth. They offer a variety of habitats for plants, animals and micro-organisms. However, forest biodiversity is increasingly threatened as a result of deforestation, fragmentation, climate change and other stressors. Biodiversity is the variation of life forms within a given ecosystem, biome, or on t...

A factorization theory is proposed for Wiener-Hopf plus Hankel operators with almost periodic Fourier symbols. We introduce a factorization concept for the almost periodic Fourier symbols such that the properties of the factors will allow corresponding operator factorizations. Conditions for left, right, or both-sided invertibility of the Wiener-Hopf plus Hankel operators are therefore obtained...

Abstract This work presents a simple method for partitioning the bond‐additive and atoms‐pair‐additive distance‐based topological indices of plane graphs into sum contributions inner faces. The proposed is applied to decompose several (Wiener, hyper‐Wiener, Tratch‐Stankevich‐Zefirov, Balaban, Szeged indices) ring series benzenoid systems. It was found that employed scheme providing an accurate ...

Among various topological indices considered in chemical graph theory, only a few have been widely studied in mathematical and chemical literatures. However, it seems that less attention has been paid to the Wiener polarity index. It was introduced by Harold Wiener1 for acyclic molecules in 1947. The Wiener polarity index of an organic molecule the molecular graph of which is G = (V,E) is defin...

quantifying spatial structure is one of the most important components, describing natural ecosystems and their biodiversity. in this study, a set of indices and functions related to spatial structure using 102 established plots with an area of 1000 m2 were presented. to achieve spatial structure of carpinus-fagus type, a set of indices (clark & evans, uniform angle, shannon-wiener, mingling and...

The eccentric sequence of a connected graph \(G\) is the nondecreasing eccentricities its vertices. Wiener index sum distances between all unordered pairs vertices \(G\). unique trees that minimise among with given were recently determined by present authors. In this paper we show these results hold not only for index, but large class distance-based topological indices which term Wiener-type in...

The Wiener index of a graph G is defined as W (G) = ∑ u,v dG(u, v), where dG(u, v) is the distance between u and v in G, and the sum goes over all pairs of vertices. In this paper, we characterize the connected unicyclic graph with minimum Wiener indices among all connected unicyclic graphs of order n and girth g with k pendent vertices.

It is proved that the Wiener index of a weighted graph (G, w) can be expressed as the sum of the Wiener indices of weighted quotient graphs with respect to an arbitrary combination of Θ∗-classes. Here Θ∗ denotes the transitive closure of the Djoković-Winkler’s relation Θ. A related result for edge-weighted graphs is also given and a class of graphs studied in [19] is characterized as partial cu...

The Wiener index, defined as the total sum of distances in a graph, is one of the most popular graph-theoretical indices. Its average value has been determined for several classes of trees, giving an asymptotics of the form Kn5/2 for some K. In this note, it is shown how the method can be extended to trees with restricted degrees. Particular emphasis is placed on chemical trees – trees with max...