20.500.12556/DKUM-66651 Corroborating a modification of the Wiener index Potvrda modifikacije Wienerova indeksa In a recent work [Chem. Phys. Lett. 333 (2001) 319-321] Nikolić, Trinajstić, and Randie put forward a novel modification ▫$^m$▫W of the Wiener index. We now show that ▫$^m$▫W possesses the basic properties required by a topological index to be acceptable as a measure of the extent of branching of the carbon-atom skeleton of the respective molecule (and therefore to be a structure-descriptor, potentially applicable in QSPR and QSAR studies). 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 mw(Pn) < mW(Tn) < mW(Sn). We also show how the concept of the modified Wiener index can be extended to weighted molecular graphs. U nedavnom su članku (Chem. Phys. Lett. 333 (2001) 319–321) Nikolić, Trinajstić i Randić predložili novu modifikaciju, ▫$^m$▫W, Wienerova indeksa. U ovom je članku pokazano da ▫$^m$▫W posjeduje osnovna svojstva koja mora imati topologijski indeks da bi bio prihvatljiv kao mjera grananja ugljikova kostura pojedine molekule (pa da bi bio primjenjiv u QSPR i QSAR modeliranju). Ako je ▫$T_n$▫ bilo koje stablo s n čvorova, koje se razlikuje od staze ▫$P_n$▫ s n čvorova i zvijezde ▫$S_n$▫ s n čvorova, tada je mw(Pn) < mW(Tn) < mW(Sn). Također je pokazano da se koncepcija o modificiranom Wienerovu indeksu može proširiti na vagane molekulske grafove. graph theory distance molecular graphs modified Wiener index weigted modified Wiener index branching chemical graph theory teorija grafov razdalja molekularni grafi kemijska teorija grafov modificiran Wienerjev indeks razvejanost true false true Angleški jezik Hrvaški jezik Znanstveno delo 2017-07-05 09:03:38 2017-07-05 09:04:36 2022-08-01 13:00:31 2019-07-11 15:54:25 2002 0 0 str. 603-612 št. 2 Letn. 75 2002 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 0011-1643 519.17 22807 7383318 0011-1643 URN:SI:UM:DK:D1EHOXOG Croatica_Chemica_Acta_2002_Gutman,_Zerovnik_Corroborating_a_modification_of_the_Wiener_index.pdf Croatica_Chemica_Acta_2002_Gutman,_Zerovnik_Corroborating_a_modification_of_the_Wiener_index.pdf 1 ACEE68E1741E7646540AD01B3E8C200C 5de6ed4f6a7a73dd6fd4c2c253eebc7edb03a6b51c7416e3bb2d4c49b52e547c 5ade2ad0-7c0e-11eb-bb7a-00155d0001ca 20.500.12556/dkum/fc4abbba-6079-43f1-8350-54ff1501cd15 https://dk.um.si/Dokument.php?lang=slv&id=113652 http://hrcak.srce.hr/127539 1 https://dk.um.si/Dokument.php?lang=slv&id=113651 Fakulteta za strojništvo 0 0 0