Altered Wiener Indices
نویسندگان
چکیده
Recently Nikolić, Trinajstić and Randić put forward a novel modification W(G) of the Wiener number W(G), called modified Wiener index , which definition was generalized later by Gutman and the present authors. Here we study another class of modified indices defined as Wmin,λ(G)=∑(V(G) mG(u,ν) −mG(u,ν) ) and show that some of the important properties of W(G), W(G) and W(G) are also properties of Wmin,λ(G), valid for most values of the parameter λ. In particular, if Tn is any n-vertex tree, different from the n-vertex path Pn and the n-vertex star Sn , then for any λ≥1 or λ < 0, Wmin,λ(Pn)>Wmin,λ(Tn)>Wmin,λ(Sn). Thus for these values of the parameter λ, Wmin,λ(G) provides a novel class of structure-descriptors, suitable for modeling branching-dependent properties of organic compounds, applicable in QSPR and QSAR studies. We also demonstrate that if trees are ordered with regard to Wmin,λ(G) then, in the general case, this ordering is different for different λ.
منابع مشابه
On terminal wiener indices of kenograms and plerograms
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...
متن کاملWiener Indices of Binary Trees
One of the most widely known topological index is the Wiener index. The Wiener Index Conjecture states that all positive integer numbers except a finite set are the Wiener indices of some trees. We explore the Wiener indices of the binary trees. We present efficient algorithms for generating the Wiener indices of the binary trees. Based on experiments we strengthen the conjecture for the class ...
متن کاملOn the edge reverse Wiener indices of TUC4C8(S) nanotubes
The edge versions of reverse Wiener indices were introduced by Mahmiani et al. very recently. In this paper, we find their relation with ordinary (vertex) Wiener index in some graphs. Also, we compute them for trees and TUC4C8(s) naotubes.
متن کاملSome results on vertex-edge Wiener polynomials and indices of graphs
The vertex-edge Wiener polynomials of a simple connected graph are defined based on the distances between vertices and edges of that graph. The first derivative of these polynomials at one are called the vertex-edge Wiener indices. In this paper, we express some basic properties of the first and second vertex-edge Wiener polynomials of simple connected graphs and compare the first and second ve...
متن کاملThe Wiener Related Indices of Some Graph Operations
The Wiener index of a connected graph G, denoted by W(G) , is defined as ∑ ( , ) , ∈ ( ) .Similarly, hyper-Wiener index of a connected graph G,denoted by WW(G), is defined as ( ) + ∑ ( , ) , ∈ ( ) .In this paper, we present the explicit formulae for the Wiener, hyper-Wiener and reverse Wiener indices of some graph operations. Using the results obtained here, the exact formulae for Wiener, hyper...
متن کاملRelation Between Wiener, Szeged and Detour Indices
In theoretical chemistry, molecular structure descriptors are used to compute properties of chemical compounds. Among them Wiener, Szeged and detour indices play significant roles in anticipating chemical phenomena. In the present paper, we study these topological indices with respect to their difference number.
متن کامل