| Autor: |
Beeler Robert A., Haynes Teresa W., Murphy Kyle |
| Jazyk: |
angličtina |
| Rok vydání: |
2019 |
| Předmět: |
|
| Zdroj: |
Discussiones Mathematicae Graph Theory, Vol 39, Iss 2, Pp 575-588 (2019) |
| Druh dokumentu: |
article |
| ISSN: |
2083-5892 |
| DOI: |
10.7151/dmgt.2102 |
| Popis: |
Let G be a graph with vertex set V and a distribution of pebbles on the vertices of V. A pebbling move consists of removing two pebbles from a vertex and placing one pebble on a neighboring vertex, and a rubbling move consists of removing a pebble from each of two neighbors of a vertex v and placing a pebble on v. We seek an initial placement of a minimum total number of pebbles on the vertices in V, so that no vertex receives more than one pebble and for any given vertex v ∈ V, it is possible, by a sequence of pebbling and rubbling moves, to move at least one pebble to v. This minimum number of pebbles is the 1-restricted optimal rubbling number. We determine the 1-restricted optimal rubbling numbers for Cartesian products. We also present bounds on the 1-restricted optimal rubbling number. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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