Naslov
A Class of Modified Wiener Indices

Autori
Gutman, I. ; Vukičević, Damir ; Žerovnik, J.

Izvornik
Croatica chemica acta (0011-1643) 77 (2004); 103-109

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Wiener index; Modified wiener index; Nikolic-trinajstic-randic index branching; Chemical graph theory

Sažetak
The Wiener index of a tree T obeys the relation W(T) = Sigma(e) n(1)(e) (.) n(2)(e) where n(1)(e) and n(2)(e) are the number of vertices on the two sides of the edge e, and where the summation goes over all edges of T. Recently Nikolic, Trinajstic and Randic put forward a novel modification W-m of the Wiener index, defined as W-m(T) = Sigma(e) [n(1)(e) (.) n(2)(e)](-1). We now extend their definition as W-m(lambda)(T) = Sigma(e) [n(1)(e) (.) n(2)(e)](lambda), and show that some of the main properties of both W and W-m are, in fact, properties of W-m(lambda), valid for all values of the parameter lambda not equal 0. In particular, if T-n is any n-vertex tree, different from the n-vertex path P-n and the n-vertex star S-n, then for any positive lambda, W-m(lambda)(P-n) > W-m(lambda)(T-n) > W-m(lambda)(S-n), whereas for any negative lambda, W-m(lambda)(P-n) < W-m(lambda)(T-n) < W-m(lambda)(S-n). Thus W-m(lambda) 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 W-m(lambda) then, in the general case, this ordering is different for different lambda

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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