Functional diversity is considered a key link between ecosystem functions and biodiversity, forms the basis for making community conservation strategies. Here, we chose subtropical forest in China as research object, which unique that other regions of world at same latitude have almost no vegetation cover. We measured 17 functional traits 100 plant species calculated seven different indices, ba...

The Hosoya polynomial of a graph, H(G, z), has the property that its first derivative, evaluated at z = 1, equals the Wiener index, i.e., W(G) = H’(G, 1). In this paper, an equation is presented that gives the hyper-Wiener index, WW(G), in terms of the first and second derivatives of H(G,z). Also defined here is a hyper-Hosoya polynomial, HH(G,r), which has the property WW(G) = HH’(G, l), analo...

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.

evaluating the quality and quantity of water resources is crucial for a sustainable development. one of the simplest methods that is able to indicate the conditions of water quality in a short period and at a low cost, compared with the physicochemical methods, is by using the biological water quality indices. identifying the contamination of water resources using biomarkers, especially indices...

Let G be a simple graph with vertex set and edge set . The function which assigns to each pair of vertices in , the length of minimal path from to , is called the distance function between two vertices. The distance function between and edge and a vertex is where for and. , . The Wiener index of a graph is denoted by and is defined by .In general this kind of index is called a topological index...

We provide a physical interpretation of the Kirchhoff index of any molecules as well as of the Wiener index of acyclic ones. For the purpose, we use a local vertex invariant that is obtained from first principles and describes the atomic displacements due to small vibrations/oscillations of atoms from their equilibrium positions. In addition, we show that the topological atomic displacements co...

In this note, we derive the lower bound on the sum for Wiener index of bipartite graph and its bipartite complement, as well as the lower and upper bounds on this sum for the Randić index and Zagreb indices. We also discuss the quality of these bounds.

Some new relations have been established between Wiener indices, stability numbers and clique numbers for several classes of composite graphs that arise via graph products. For three of considered operations we show that they make a multiplicative pair with the clique number. 2010 Mathematics Subject Classification: 05C40, 05C90