On t-Restricted Optimal Rubbling of Graphs
Institution: | East Tennessee State University |
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Department: | |
Year: | 2017 |
Keywords: | graph theory; pebbling; rubbling; Discrete Mathematics and Combinatorics |
Posted: | 02/01/2018 |
Record ID: | 2151563 |
Full text PDF: | https://dc.etsu.edu/etd/3251 |
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.