For a graph G=(V,E), we consider placing a variable number of pebbles on the vertices of V. A pebbling move consists of deleting two pebbles from a vertex u∈V and placing one pebble on a vertex v adjacent to u. We seek an initial placement of a minimum total number of pebbles on the vertices in V, so that no vertex receives more than some positive integer t pebbles and for any given vertex v∈V, it is possible, by a sequence of pebbling moves, to move at least one pebble to v. We relate this minimum number of pebbles to several other well-studied parameters of a graph G, including the domination number, the optimal pebbling number, and the Roman domination number of G.
Identifer | oai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etsu-works-11911 |
Date | 20 April 2017 |
Creators | Chellali, Mustapha, Haynes, Teresa W., Hedetniemi, Stephen T., Lewis, Thomas M. |
Publisher | Digital Commons @ East Tennessee State University |
Source Sets | East Tennessee State University |
Detected Language | English |
Type | text |
Source | ETSU Faculty Works |
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