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A Class of Modified Wiener Indices
; Faculty of Science, University of Kragujevac, 34000 Kragujevac, Serbia and Montenegro
; Department of Mathematics, University of Split, Croatia
; Faculty of Mechanical Engineering, University of Maribor, Smetanova 17, SI-2000 Maribor, Slovenia
Puni tekst: engleski, pdf (125 KB)
Gutman, I., Vukičević, D., Žerovnik, J. (2004). A Class of Modified Wiener Indices. Croatica Chemica Acta, 77(1-2), 103-109. Preuzeto s https://hrcak.srce.hr/102652
The Wiener index of a tree T obeys the relation W(T) = Σen1(e) • n2(e) where n1(e) and n2(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 Nikolić, Trinajstić and Randić put forward a novel modification mW of the Wiener index, defined as mW(T) = Σe[n1(e) • n2(e)]–1. We now extend their definition as mWλ(T) = Σe[n1(e) • n2(e)]λ, and show that some of the main properties of both W and mW are, in fact, properties of mWλ, valid for all values of the parameter λ≠0. 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 positive λ, mWλ(Pn) > mWλ(Tn) > mWλ(Sn), whereas for any negative λ, mWλ(Pn) < mWλ(Tn) < mWλ(Sn). Thus mWλ 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 mWλ then, in the general case, this ordering is different for different λ.
Wiener index; modified Wiener index; Nikolić-Trinajstić-Randić index; branching; chemical graph theory
Hrčak ID: 102652
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