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5. The Graovac-Pisanski index of connected bipartite graphs with applications to hydrocarbon moleculesMatevž Črepnjak, Martin Knor, Niko Tratnik, Petra Žigert Pleteršek, 2021, izvirni znanstveni članek Opis: 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.
Ključne besede: modified Wiener index, Graovac-Pisanski index, graph distance, automorphism group, hydrocarbons, carbon nanostructures
Objavljeno v DKUM: 14.02.2025; Ogledov: 0; Prenosov: 4
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6. Resonance graphs of plane bipartite graphs as daisy cubesSimon Brezovnik, Zhongyuan Che, Niko Tratnik, Petra Žigert Pleteršek, 2025, izvirni znanstveni članek Ključne besede: daisy cube, fries number, peripherally 2-colorable, plane (weakly) elementary bipartite graph, resonance graph
Objavljeno v DKUM: 31.01.2025; Ogledov: 0; Prenosov: 1
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7. Zagreb root-indices of graphs with chemical applicationsNiko Tratnik, Petra Žigert Pleteršek, 2024, izvirni znanstveni članek Opis: Root-indices of graphs are mathematical tools that help us to understand complex systems, like molecules and networks, by capturing key structural information. In this study, we introduce two new root-indices, the first and the second Zagreb root-index, and we analyze their properties. We apply these indices to chemical structures like benzenoid molecules and octane isomers, showing that they sometimes provide better insights than traditional indices. We also compare the effectiveness of several root-indices with their standard versions, highlighting their ability to distinguish between different graph structures.
Ključne besede: first Zagreb index, second Zagreb index, root-indices, octane isomers, discrimination power
Objavljeno v DKUM: 19.12.2024; Ogledov: 0; Prenosov: 7
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8. Resonance graphs and a binary coding of perfect matchings of outerplane bipartite graphsSimon Brezovnik, Niko Tratnik, Petra Žigert Pleteršek, 2023, izvirni znanstveni članek Opis: The aim of this paper is to investigate resonance graphs of $2$-connected outerplane bipartite graphs, which include various families of molecular graphs. Firstly, we present an algorithm for a binary coding of perfect matchings of these graphs. Further, $2$-connected outerplane bipartite graphs with isomorphic resonance graphs are considered. In particular, it is shown that if two $2$-connected outerplane bipartite graphs are evenly homeomorphic, then its resonance graphs are isomorphic. Moreover, we prove that for any $2$-connected outerplane bipartite graph $G$ there exists a catacondensed even ring systems $H$ such that the resonance graphs of $G$ and $H$ are isomorphic. We conclude with the characterization of $2$-connected outerplane bipartite graphs whose resonance graphs are daisy cubes.
Ključne besede: graph theory, resonance graphs, bipartite graphs
Objavljeno v DKUM: 10.12.2024; Ogledov: 0; Prenosov: 11
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9. Učni načrtMarjeta Kovač, Nives Markun Puhan, Breda Lorenci, Leonida Novak, Jurij Planinšec, Iztok Hrastar, Karmen Pleteršek, Vesna Muha, 2011, strokovna monografija Opis: Učni načrt
Ključne besede: športna vzgoja, osnovna šola, učni načrt
Objavljeno v DKUM: 12.09.2024; Ogledov: 27; Prenosov: 9
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10. Weighted wiener indices of molecular graphs with application to alkenes and alkadienesSimon Brezovnik, Niko Tratnik, Petra Žigert Pleteršek, 2021, izvirni znanstveni članek Opis: There exist many topological indices that are calculated on saturated hydrocarbons since they can be easily modelled by simple graphs. On the other hand, it is more challenging to investigate topological indices for hydrocarbons with multiple bonds. The purpose of this paper is to introduce a simple model that gives good results for predicting physico-chemical properties of alkenes and alkadienes. In particular, we are interested in predicting boiling points of these molecules by using the well known Wiener index and its weighted versions. By performing the non-linear regression analysis we predict boiling points of alkenes and alkadienes.
Ključne besede: weighted Wiener index, alkenes, alkadienes, boiling point
Objavljeno v DKUM: 30.05.2024; Ogledov: 115; Prenosov: 15
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