34 KB991 KB24 KB199820252005Vukičević, DamirŽerovnik, Janez10 straništevilka:3letnik:52str. 272-281ISSN:1318-0207COBISSID:9929238URN:URN:NBN:SI:doc-Y6YMRBT1enSlovensko kemijsko društvoActa chimica slovenicachemistrykemijamatematikamathematicsteorija grafovtopološki indeksiWienerjev indeksAltered Wiener indices|Recently Nikolić, Trinajstič and Randić put forward a novel modification ?$^mW(G)$? of the Wiener index ?$W(G)$?, defined as ?$^mW(G) = \sum_{u,v \in E(G)} n_G(u,v)^{-1} n_G(v,u)^{-1}$?. This definition was generalized to $^mW(G) = \sum_{u,v \in E(G)} n_G(u,v)^{\lambda} n_G(v,u)^{\lamba}$ by Gutman and the present authors. Another class of modified indices ?$_{\lambda$}W(G) = \frac{1}{2} \sum_{uv \in E(G)} (v(G)^\lammda - n_G(u,v)^\lambda - n_G(v,u)^\lambda)$? is studied here. It is shown that some of main properties of ?$W(G)$?, $^mW(G)$ and $^{\lambda}W(G)$ are also properties of $_{\lambda}W(G)$, valid for all values of the parameter ?$\lambda \ne 0$?. 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 ?$\lambda > 1$?, ?$_\lambda W(P_n) > _\lambda W(T_n) > \lambda W(S_n)$?, vhereas for any ?$\lambda <1$?, $_\lambda W(P_n) < _\lambda W(T_n) < \lambda W(S_n)$. Thus ?$_\lambda W(G)$? 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 ?$_\lambda W(G)$? then, in the general case, this ordering is different for different ?$\lambda$?TEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaSlovensko kemijsko društvo