| Autor: |
LeRoy B. Beasley, Jeong Han Kim, Seok-Zun Song |
| Jazyk: |
angličtina |
| Rok vydání: |
2019 |
| Předmět: |
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| Zdroj: |
Mathematics, Vol 7, Iss 4, p 312 (2019) |
| Druh dokumentu: |
article |
| ISSN: |
2227-7390 |
| DOI: |
10.3390/math7040312 |
| Popis: |
A graph has genus k if it can be embedded without edge crossings on a smooth orientable surface of genus k and not on one of genus k − 1 . A mapping of the set of graphs on n vertices to itself is called a linear operator if the image of a union of graphs is the union of their images and if it maps the edgeless graph to the edgeless graph. We investigate linear operators on the set of graphs on n vertices that map graphs of genus k to graphs of genus k and graphs of genus k + 1 to graphs of genus k + 1 . We show that such linear operators are necessarily vertex permutations. Similar results with different restrictions on the genus k preserving operators give the same conclusion. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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