| Title: | The Graovac-Pisanski index of connected bipartite graphs with applications to hydrocarbon molecules |
|---|
| Authors: | ID Črepnjak, Matevž (Author)
ID Knor, Martin (Author)
ID Tratnik, Niko (Author)
ID Žigert Pleteršek, Petra (Author) |
|---|
| Files: |  RAZ_Crepnjak_Matevz_2021.pdf (1,36 MB)
MD5: 3342A236EEA894C980C7C0FE501BAEA7
 https://doi.org/10.1080/1536383X.2021.1910675
|
|---|
| Language: | English |
|---|
| Work type: | Scientific work |
|---|
| Typology: | 1.01 - Original Scientific Article |
|---|
| Organization: | FNM - Faculty of Natural Sciences and Mathematics
FKKT - Faculty of Chemistry and Chemical Engineering
|
|---|
| Abstract: | 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. |
|---|
| Keywords: | modified Wiener index, Graovac-Pisanski index, graph distance, automorphism group, hydrocarbons, carbon nanostructures |
|---|
| Publication status: | Published |
|---|
| Publication version: | Version of Record |
|---|
| Submitted for review: | 20.03.2021 |
|---|
| Article acceptance date: | 26.03.2021 |
|---|
| Publication date: | 22.04.2021 |
|---|
| Year of publishing: | 2021 |
|---|
| Number of pages: | str. 884-889 |
|---|
| Numbering: | Letn. 29, št. 11 |
|---|
| PID: | 20.500.12556/DKUM-89008  |
|---|
| UDC: | 519.17 |
|---|
| ISSN on article: | 1536-383X |
|---|
| COBISS.SI-ID: | 61003523 |
|---|
| DOI: | 10.1080/1536383X.2021.1910675 |
|---|
| Publication date in DKUM: | 14.02.2025 |
|---|
| Views: | 159 |
|---|
| Downloads: | 14 |
|---|
| Metadata: |    |
|---|
| Categories: | Misc.
|
|---|
|
:
|
Copy citation |
|---|
| | | | Average score: | (0 votes) |
|---|
| Your score: | Voting is allowed only for logged in users. |
|---|
| Share: |  |
|---|
Hover the mouse pointer over a document title to show the abstract or click
on the title to get all document metadata. |
