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arXiv · 1909.01703

A note on the optimal rubbling in ladders and prisms

Zheng-Jiang Xia·Zhen-Mu Hong
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Abstract

A pebbling move on a graph G consists of the removal of two pebbles from one vertex and the placement of one pebble on an adjacent vertex. Rubbling is a version of pebbling where an additional move is allowed, which is also called the strict rubbling move. In this new move, one pebble each is removed from u and v adjacent to a vertex w, and one pebble is added on w. The optimal rubbling number of a graph G is the smallest number m, such that one pebble can be moved to every given vertex from some pebble distribution of m pebbles by a sequence of rubbling moves. In this paper, we give short proofs to determine the rubbling number of cycles and the optimal rubbling number of paths, cycles, ladders, prisms and Mobius-ladders.

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Zheng-Jiang Xia, Zhen-Mu Hong. 2019-09-04. A note on the optimal rubbling in ladders and prisms. https://arxiv.org/abs/1909.01703

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