All Pairs of Pentagons in Leapfrog Fullerenes Are Nice
A subgraph <i>H</i> of a graph <i>G</i> with perfect matching is nice if <inline-formula><math display="inline"><semantics><mrow><mi>G</mi><mo>−</mo><mi>V</mi><mo>(</mo><mi>H</mi><...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/12/2135 |
| _version_ | 1827701042278563840 |
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| author | Tomislav Došlić |
| author_facet | Tomislav Došlić |
| author_sort | Tomislav Došlić |
| collection | DOAJ |
| description | A subgraph <i>H</i> of a graph <i>G</i> with perfect matching is nice if <inline-formula><math display="inline"><semantics><mrow><mi>G</mi><mo>−</mo><mi>V</mi><mo>(</mo><mi>H</mi><mo>)</mo></mrow></semantics></math></inline-formula> has perfect matching. It is well-known that all fullerene graphs have perfect matchings and that all fullerene graphs contain some small connected graphs as nice subgraphs. In this contribution, we consider fullerene graphs arising from smaller fullerenes via the leapfrog transformation, and show that in such graphs, each pair of (necessarily disjoint) pentagons is nice. That answers in affirmative a question posed in a recent paper on nice pairs of odd cycles in fullerene graphs. |
| first_indexed | 2024-03-10T14:25:12Z |
| format | Article |
| id | doaj.art-6055501a8bad4c959d52bb2295d1eb46 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T14:25:12Z |
| publishDate | 2020-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-6055501a8bad4c959d52bb2295d1eb462023-11-20T23:04:47ZengMDPI AGMathematics2227-73902020-12-01812213510.3390/math8122135All Pairs of Pentagons in Leapfrog Fullerenes Are NiceTomislav Došlić0Faculty of Civil Engineering, University of Zagreb, Kačićeva 26, 10000 Zagreb, CroatiaA subgraph <i>H</i> of a graph <i>G</i> with perfect matching is nice if <inline-formula><math display="inline"><semantics><mrow><mi>G</mi><mo>−</mo><mi>V</mi><mo>(</mo><mi>H</mi><mo>)</mo></mrow></semantics></math></inline-formula> has perfect matching. It is well-known that all fullerene graphs have perfect matchings and that all fullerene graphs contain some small connected graphs as nice subgraphs. In this contribution, we consider fullerene graphs arising from smaller fullerenes via the leapfrog transformation, and show that in such graphs, each pair of (necessarily disjoint) pentagons is nice. That answers in affirmative a question posed in a recent paper on nice pairs of odd cycles in fullerene graphs.https://www.mdpi.com/2227-7390/8/12/2135perfect matchingnice subgraphfullerene graphleapfrog fullerene |
| spellingShingle | Tomislav Došlić All Pairs of Pentagons in Leapfrog Fullerenes Are Nice Mathematics perfect matching nice subgraph fullerene graph leapfrog fullerene |
| title | All Pairs of Pentagons in Leapfrog Fullerenes Are Nice |
| title_full | All Pairs of Pentagons in Leapfrog Fullerenes Are Nice |
| title_fullStr | All Pairs of Pentagons in Leapfrog Fullerenes Are Nice |
| title_full_unstemmed | All Pairs of Pentagons in Leapfrog Fullerenes Are Nice |
| title_short | All Pairs of Pentagons in Leapfrog Fullerenes Are Nice |
| title_sort | all pairs of pentagons in leapfrog fullerenes are nice |
| topic | perfect matching nice subgraph fullerene graph leapfrog fullerene |
| url | https://www.mdpi.com/2227-7390/8/12/2135 |
| work_keys_str_mv | AT tomislavdoslic allpairsofpentagonsinleapfrogfullerenesarenice |