1-Restricted Optimal Rubbling on Graphs

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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 vV, 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.

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Discussiones Mathematicae Graph Theory

The Journal of University of Zielona Góra

Journal Information

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Target Group

researchers in the fields of: colourings, partitions (general colourings), hereditary properties, independence and dominating structures (sets, paths, cycles, etc.), cycles, local properties, products of graphs


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