| Title: | Altered Wiener indices |
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| Authors: | ID Vukičević, Damir (Author)
ID Žerovnik, Janez (Author) |
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| Files: |  Acta_Chimica_Slovenica_2005_Vukicevic,_Zerovnik_Altered_Wiener_indices.pdf (991,46 KB)
MD5: FF0DC1E906D57B7B7E47A6B564EC003F
PID: 20.500.12556/dkum/ed676b34-d981-4cb2-b2e3-70790f465af2
 http://acta-arhiv.chem-soc.si/52/52-3-272.pdf
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| Language: | English |
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| Work type: | Scientific work |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FS - Faculty of Mechanical Engineering
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| Abstract: | Recently Nikolić, Trinajstić and Randić put forward a novel modification ▫$^mW(G)$▫ 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 ▫$W_{min,λ}(G) = ∑(V(G)^λm_G(u,ν)^λ−m_G(u,ν)^{2λ})$▫ and show that some of the important properties of ▫$W(G)$▫, ▫$^mW(G)$▫ and ▫$^λW(G)$▫ are also properties of ▫$W_{min,λ}(G)$▫, valid for most values of the parameter λ. 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 λ ≥ 1 or λ < 0, ▫$^W_{min,λ}(P_n) > W_{min,λ}(T_n)>W_{min,λ}(S_n)$▫. Thus for these values of the parameter λ, ▫$W_{min,λ}(G)$▫ 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 ▫$W_{min,λ}(G)$▫ then, in the general case, this ordering is different for different λ. |
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| Keywords: | mathematics, chemical graph theory, Wiener index, modified Wiener index |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Year of publishing: | 2005 |
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| Number of pages: | str. 272-281 |
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| Numbering: | Letn. 52, št. 3 |
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| PID: | 20.500.12556/DKUM-67412  |
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| ISSN: | 1318-0207 |
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| UDC: | 519.17:54 |
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| ISSN on article: | 1318-0207 |
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| COBISS.SI-ID: | 9929238 |
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| NUK URN: | URN:SI:UM:DK:3UGNDLNW |
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| Publication date in DKUM: | 17.08.2017 |
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| Views: | 1494 |
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| Downloads: | 136 |
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| Metadata: |    |
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| Categories: | Misc.
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