20.500.12556/DKUM-66646 A class of modified Wiener indices Jedna klasa modificiranih Wienerovih indeksa 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. Wienerov indeks stabla T zadovoljava relaciju W(T) = ∑e n1(e) ·n2(e) gdje su n1(e) i n2(e) broj čvorova na dvije strane grane e, i gdje sumiranje ide preko svih grana stabla T. Nedavno su Nikolić, Trinajstić i Randić predložili modifikaciju mW Wienerovog indeksa, definiranu kao mW(T) = ∑e [ n1(e) ·n2(e) ]^–1. Mi sada proširujemo njihovu definiciju na mW λ (T) = ∑e [ n1(e) ·n2(e) ]^λ, i pokazujemo da neka od važnijih svojstava kako W tako i mW važe za mW λ, za svaku vrijednost parametra λ ≠ 0. Ako je Tn bilo koje stablo s n čvorova, različito od puta Pn i zvijezde Sn, onda za svaku pozitivnu λ, mW λ (Pn) > mW λ (Tn) > mW λ (Sn), dok za svaku negativnu λ, mW λ (Pn) < mWß(Tn) < mW λ (Sn). Na taj način mW λ predstavlja novu klasu strukturnih deskriptora, pogodnih za modeliranje o razgranatosti ovisnih svojstava organskih spojeva i učinkovitih u QSPR i QSAR studijama. Također pokazujemo da ako su stabla uređena prema mW λ, tada se, u općem slučaju, ovaj uređaj razlikuje za različite λ. graph theory chemical graph theory modified Wiener index Nikolić-Trinajstić-Randić index branching teorija grafov kemijska teorija grafov modificiran Wienerjev indeks indeks Nikolić-Trinajstić-Randić razvejanost true false true Angleški jezik Hrvaški jezik Znanstveno delo 2017-07-05 08:26:23 2017-07-05 08:29:23 2022-08-01 13:00:11 2019-07-11 15:54:15 2004 0 0 str. 103-109 št. 1/2 Letn. 77 2004 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 0011-1643 519.17 22807 9803798 0011-1643 URN:SI:UM:DK:C3PO2HSK Croatica_Chemica_Acta_2004_Gutman,_Vukicevic,_Zerovnik_A_Class_of_Modified_Wiener_Indices.pdf Croatica_Chemica_Acta_2004_Gutman,_Vukicevic,_Zerovnik_A_Class_of_Modified_Wiener_Indices.pdf 1 E825E1E26A9D73DBB71A0997FD1764F4 653ef7ccc89558881c3cb46700cb0e2629d8d3af96a6af8f9661b52b708a57fc 5a91cea5-7c0e-11eb-bb7a-00155d0001ca 20.500.12556/dkum/1e8aa100-0e43-42ec-81ca-162f8bbcbc55 https://dk.um.si/Dokument.php?lang=slv&id=113641 http://hrcak.srce.hr/102652 1 https://dk.um.si/Dokument.php?lang=slv&id=113640 Fakulteta za strojništvo 0 0 0