| Title: | A class of modified Wiener indices |
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| Authors: | ID Gutman, Ivan (Author)
ID Vukičević, Damir (Author)
ID Žerovnik, Janez (Author) |
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| Files: |  Croatica_Chemica_Acta_2004_Gutman,_Vukicevic,_Zerovnik_A_Class_of_Modified_Wiener_Indices.pdf (125,08 KB)
MD5: E825E1E26A9D73DBB71A0997FD1764F4
PID: 20.500.12556/dkum/1e8aa100-0e43-42ec-81ca-162f8bbcbc55
 http://hrcak.srce.hr/102652
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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: | 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. |
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| Keywords: | graph theory, chemical graph theory, modified Wiener index, Nikolić-Trinajstić-Randić index, branching |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Year of publishing: | 2004 |
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| Number of pages: | str. 103-109 |
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| Numbering: | Letn. 77, št. 1/2 |
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| PID: | 20.500.12556/DKUM-66646  |
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| ISSN: | 0011-1643 |
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| UDC: | 519.17 |
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| ISSN on article: | 0011-1643 |
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| COBISS.SI-ID: | 9803798 |
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| NUK URN: | URN:SI:UM:DK:C3PO2HSK |
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| Publication date in DKUM: | 05.07.2017 |
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| Views: | 1351 |
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| Downloads: | 115 |
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| Metadata: |    |
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| Categories: | Misc.
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