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...

Whereas there is an exact linear relation between the Wiener indices of kenograms and plerograms of isomeric alkanes, the respective terminal Wiener indices exhibit a completely different behavior: Correlation between terminal Wiener indices of kenograms and plerograms is absent, but other regularities can be envisaged. In this article, we analyze the basic properties of terminal Wiener indices...

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,...

We prove a conjecture of Nadjafi-Arani et al. on the difference between the Szeged and the Wiener index of a graph (M. J. Nadjafi-Arani, H. Khodashenas, A. R. Ashrafi: Graphs whose Szeged and Wiener numbers differ by 4 and 5, Math. Comput. Modelling 55 (2012), 1644–1648). Namely, if G is a 2-connected non-complete graph on n vertices, then Sz (G) −W (G) ≥ 2n − 6. Furthermore, the equality is ob...

The Wiener index W( G) of a connected graph G is the sum of the distances d( u, v) between all pairs of vertices u and v of G. This index seems to have been introduced in [22] where it was shown that certain physical properties of various paraffin species are correlated with the Wiener index of the tree determined by the carbon atoms of the corresponding molecules. Canfield, Robinson, and Rouvr...

we derived explicit formulae for the eccentric connectivity index and wiener index of2-dimensional square-octagonal tuc4c8(r) lattices with open and closed ends. newcompression factors for both indices are also computed in the limit n-->∞.

7 n 2  ≤ WW (G1) + WW (G2) + WW (G3) ≤ 2  n + 2 4  + n 2  + 4(n − 1). The corresponding extremal graphs are characterized. Published by Elsevier B.V.

Let G be a graph. The Wiener index of G, W (G), is defined as the sum of distances between all pairs of vertices of G. Denote by L i (G) its i-iterated line graph. In the talk, we will consider the equation W (L i (T)) = W (T) where T is a tree and i ≥ 1.

The Wiener index W(G) of a connected graph G is defined as the sum of the distances between all unordered pairs of vertices of G. The eccentricity of a vertex v in G is the distance to a vertex farthest from v. In this paper we obtain the Wiener index of a graph in terms of eccentricities. Further we extend these results to the self-centered graphs.