Knjižnica tehniških fakultet, Maribor (KTFMB)
  • Altered Wiener indices
    Vukičević, Damir ; Žerovnik, Janez, 1958-
    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 ▫$\lambda$▫.
    Vir: Acta chimica slovenica. - ISSN 1318-0207 (Vol. 52, no. 3, 2005, str. 272-281)
    Vrsta gradiva - članek, sestavni del
    Leto - 2005
    Jezik - angleški
    COBISS.SI-ID - 9929238

    Povezava(-e):

    Digitalna knjižnica Univerze v Mariboru – DKUM
    Digitalna knjižnica Slovenije - dLib.si

vir: Acta chimica slovenica. - ISSN 1318-0207 (Vol. 52, no. 3, 2005, str. 272-281)

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