2-pebbling property of butterfly-derived graphs (Q2113781)

Summary: For a graph \(G\), \(f(G)\) is the least distribution of \(p\) pebbles on the vertices of \(G\), so that we can move a pebble to any vertex by a sequence of moves and each move is taking two pebbles off one vertex and placing one pebble on an adjacent vertex. A graph \(G\) is said to satisfy 2-pebbling property, if it is possible to move two pebbles to any arbitrarily chosen vertex with a possible distribution of \(2f(G) - q + 1\) pebbles, where \(q\) is the number of vertices with at least one pebble. This paper determines the pebbling number and the 2-pebbling property of butterfly derived graphs.