The Optimal Pebbling Number of the Caterpillar
نویسندگان
چکیده
Let G be a simple graph. If we place p pebbles on the vertices of G, then a pebbling move is taking two pebbles off one vertex and then placing one on an adjacent vertex. The optimal pebbling number of G, f ′(G), is the least positive integer p such that p pebbles are placed suitably on vertices of G and for any target vertex v of G, we can move one pebble to v by a sequence of pebbling moves. In this paper, we find the optimal pebbling number of the caterpillar. Key word. Optimal pebbling, Caterpillar. AMS(MOS) subject classification. 05C05
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