Name
Abstract | ||
|---|---|---|
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 is an element of 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. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.7151/dmgt.2102 | DISCUSSIONES MATHEMATICAE GRAPH THEORY |
Keywords | Field | DocType |
graph pebbling,graph rubbling,optimal rubbling,t-restricted optimal pebbling | Discrete mathematics,Graph,Combinatorics,Mathematics | Journal |
Volume | Issue | ISSN |
39 | 2 | 1234-3099 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Robert A. Beeler | 1 | 11 | 4.04 |
| Teresa W. Haynes | 2 | 774 | 94.22 |
| Kyle Murphy | 3 | 0 | 0.34 |