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...

Quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies use statistical models to compute physical, chemical, or biological properties of a chemical substance from its molecular structure, encoded in a numerical form with the aid of various descriptors. Structural indices derived from molecular graph matrices represent an important gro...

The sum of distances between all vertices pairs in a connected graph is known as the Wiener Index. It is the earliest of the indices that correlates well with many physicochemical properties of organic compounds and as such has been well-studied over the last quarter of a century. A q-analogue of this index, termed the Wiener Polynomial by Hosoya but also known today as the Hosoya Polynomial, e...

We find the extremal values of the energy, the Wiener index and several vertex-degree-based topological indices over the set of Kragujevac trees with the central vertex of fixed degree. 2010 Mathematics Subject Classification : 05C90, 05C35.

two sides of the edge e, and where the summation goes over all edges of T . The λ -modified Wiener index is defined as Wλ (T ) = ∑ e [nT,1(e) · nT,2(e)] . For each λ > 0 and each integer d with 3 ≤ d ≤ n− 2, we determine the trees with minimal λ -modified Wiener indices in the class of trees with n vertices and diameter d. The reverse Wiener index of a tree T with n vertices is defined as Λ (T)...

Let G be a graph. The distance d(u,v) between the vertices u and v of the graph G is equal to the length of a shortest path that connects u and v. The Wiener index W(G) is the sum of all distances between vertices of G, whereas the hyper-Wiener index WW(G) is defined as WW(G)=12W(G)+12@?"{"u","v"}"@?"V"("G")d (u,v)^2. In this paper the hyper-Wiener indices of the Cartesian product, composition,...