淡江大學機構典藏:Item 987654321/41257
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    Please use this identifier to cite or link to this item: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/41257


    Title: Generalized Wiener indices in hexagonal chains
    Other Titles: 計算六角環鍊的推廣 Wiener 指數
    Authors: 游森棚;Eu, Sen-peng;楊柏因;Yang, Bo-yin;葉永南;Yeh, Yeong-nan
    Contributors: 淡江大學數學學系
    Date: 2006-01-01
    Issue Date: 2010-01-28 07:06:07 (UTC+8)
    Publisher: Wiley-Blackwell
    Abstract: The Wiener index, or the Wiener number, also known as the “sum of distances” of a connected graph, is one of the quantities associated with a molecular graph that correlates nicely to physical and chemical properties, and has been studied in depth. An index proposed by Schultz is shown to be related to the Wiener index for trees, and Ivan Gutman proposed a modification of the Schultz index with similar properties. We deduce a similar relationship between these three indices for catacondensed benzenoid hydrocarbons (graphs formed of concatenated hexagons, or hexagonal chains, or sometimes acenes). Indeed, we may define three families of generalized Wiener indices, which include the Schultz and Modified Schultz indices as special cases, such that similar explicit formulae for all generalized Wiener indices hold on hexagonal chains. We accomplish this by first giving a more refined proof of the formula for the standard Wiener index of a hexagonal chain, then extending it to the generalized Wiener indices via the notion of partial Wiener indices. Finally, we discuss possible extensions of the result.
    Relation: International Journal of Quantum Chemistry 106(2), pp.426-435
    DOI: 10.1002/qua.20732
    Appears in Collections:[Graduate Institute & Department of Mathematics] Journal Article

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