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- Title
1-RESTRICTED OPTIMAL RUBBLING ON GRAPHS.
- Authors
BEELER, ROBERT A.; HAYNES, TERESA W.; MURPHY, KYLE
- 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 ϵ 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..
- Subjects
GRAPH connectivity; BIPARTITE graphs; ISOMORPHISM (Mathematics); SUBGRAPHS; DIRECTED graphs
- Publication
Discussiones Mathematicae: Graph Theory, 2019, Vol 39, Issue 2, p575
- ISSN
1234-3099
- Publication type
Article
- DOI
10.7151/dmgt.2102