On t-Restricted Optimal Rubbling of Graphs
For a graph G = (V;E), a pebble distribution is defined as a mapping of the vertex set in to the integers, where each vertex begins with f(v) pebbles. A pebbling move takes two pebbles from some vertex adjacent to v and places one pebble on v. A rubbling move takes one pebble from each of two vertic...
| Main Author: | |
|---|---|
| Format: | Others |
| Language: | English |
| Published: |
Digital Commons @ East Tennessee State University
2017
|
| Subjects: | |
| Online Access: | https://dc.etsu.edu/etd/3251 https://dc.etsu.edu/cgi/viewcontent.cgi?article=4685&context=etd |
| Summary: | For a graph G = (V;E), a pebble distribution is defined as a mapping of the vertex set in to the integers, where each vertex begins with f(v) pebbles. A pebbling move takes two pebbles from some vertex adjacent to v and places one pebble on v. A rubbling move takes one pebble from each of two vertices that are adjacent to v and places one pebble on v. A vertex x is reachable under a pebbling distribution f if there exists some sequence of rubbling and pebbling moves that places a pebble on x. A pebbling distribution where every vertex is reachable is called a rubbling configuration. The t-restricted optimal rubbling number of G is the minimum number of pebbles required for a rubbling configuration where no vertex is initially assigned more than t pebbles. Here we present results on the 1-restricted optimal rubbling number and the 2- restricted optimal rubbling number. |
|---|