Including or excluding rare taxa in bioassessment is a controversial topic, which essentially affects the reliability and accuracy of the result. In the present paper, we hypothesize that biological indices such as Shannon-Wiener index, Simpson's index, Margalef index, evenness, BMWP (biological monitoring working party), and ASPT (Average Score Per Taxon) respond differently to rare taxa exclu...

By the Von Neumann regular graph of R, we mean the graph that its vertices are all elements of R such that there is an edge between vertices x,y if and only if x+y is a von Neumann regular element of R, denoted by G_Vnr (R). For a commutative ring R with unity, x in R is called Von Neumann regular if there exists x in R such that a=a2 x. We denote the set of Von Neumann regular elements by V nr...

Dendritic macromolecules’ have attracted much attention as organic examples of well-defined nanostructures. These molecules are ideal model systems for studying how physical properties depend on molecular size and architecture. In this paper using a simple result, some GAP programs are prepared to compute Wiener and hyper Wiener indices of dendrimers.

Topological indices have important role in theoretical chemistry for QSPR researches. Among the all topological indices the Randić and the Zagreb indices have been used more considerably than any other topological indices in chemical and mathematical literature. Most of the topological indices as in the Randić and the Zagreb indices are based on the degrees of the vertices of a connected graph....

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 ...

In past years, topological indices are introduced to measure the characters of chemical molecules. Thus, the study of these topological indices has raised large attention in the field of chemical science, biology science and pharmaceutical science. In this paper, by virtue of molecular structure analysis, we determine the total Szeged index, vertex-edge Wiener index and edge hyper-Wiener index ...

The Wiener index of a graph G is defined as W(G) = 1/2∑{x,y}⊆V(G)d(x,y), where V(G) is the set of all vertices of G and for x,y ∈ V(G), d(x,y) denotes the length of a minimal path between x and y. In this paper, we first report our recent results on computing Wiener, PI and Balaban indices of some nanotubes and nanotori. Next, the PI and Szeged indices of a new type of nanostar dendrimers are c...

The Wiener index of a connected graph is defined as the sum of distances between all unordered pairs of its vertices. We determine the minimum Wiener indices of trees and unicyclic graphs with given number of vertices and matching number, respectively. The extremal graphs are characterized.

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 article we state a relation between the Kirchhoff and Wiener indices of a simple connected graph G and the Kirchhoff and Wiener indices of those subgraphs of G which are induced by its blocks. Then as an application, we define a composition of a rooted tree T and a graph G and calculate its Kirchhoff index in terms of parameters of T and G. Finally, we present an algorithm for computing...