20.500.12556/DKUM-89008 The Graovac-Pisanski index of connected bipartite graphs with applications to hydrocarbon molecules The Graovac-Pisanski index, also called the modified Wiener index, was introduced in 1991 and represents an extension of the original Wiener index, because it considers beside the distances in a graph also its symmetries. Similarly as Wiener in 1947 showed the correlation of the Wiener indices of the alkane series with the boiling points, in 2018 the connection between the GraovacPisanski index and the melting points of some hydrocarbon molecules was established. In this paper, we prove that the Graovac-Pisanski index of any connected bipartite graph as well as of any connected graph on an even number of vertices is an integer number. These results are applied to some important families of hydrocarbon molecules. By using a computer programme, the graphs with a non-integer Graovac-Pisanski index on at most nine vertices are counted. Finally, an infinite class of unicyclic graphs with a non-integer Graovac-Pisanski index is described. modified Wiener index Graovac-Pisanski index graph distance automorphism group hydrocarbons carbon nanostructures modificiran Wienerjev indeks Graovac-Pisanski indeks razdalja grafov skupina avtomorfizmov ogljikovodiki ogljikove nanostrukture true false true Angleški jezik Slovenski jezik Znanstveno delo 2024-06-05 03:25:27 2025-02-14 10:50:30 2025-02-15 03:11:21 0000-00-00 00:00:00 2021 0 0 str. 884-889 št. 11 Letn. 29 2021 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2021-03-20 2021-03-26 2021-04-22 519.17 61003523 10.1080/1536383X.2021.1910675 1536-383X RAZ_Crepnjak_Matevz_2021.pdf RAZ_Crepnjak_Matevz_2021.pdf 1 3342A236EEA894C980C7C0FE501BAEA7 a2e6e89c84cb9e5747186eb80b0333816508477517ad50404a955dd86fe69583 0ae65f48-eab9-11ef-bdc3-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=188670 https://doi.org/10.1080/1536383X.2021.1910675 0 16c38752-eab9-11ef-bdc3-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=188671 Fakulteta za naravoslovje in matematiko Fakulteta za kemijo in kemijsko tehnologijo 0 0 0