2019/09/04 by Xia, Zheng-Jiang, Hong, Zhen-Mu
#05C99 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1909.01703
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.