Browsing by Subject "Pebbling"
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Item Covering cover pebbling number of products of paths(2015-05) McGahan, IanThere are a variety of pebbling numbers, such as classical pebbling number, cover pebbling number, and covering cover pebbling number. In this paper we determine the covering cover pebbling number for Cartesian products of paths. The covering cover pebbling number of a graph, G, is the smallest number of pebbles, n, required such that any distribution of n pebbles onto the vertices of G can be, through a sequence of pebbling moves, redistributed so that C, a vertex cover of G, is pebbled. Traditionally, a pebbling move is defined as the removal of two pebbles from one vertex and the placement of one pebble on an adjacent vertex. In this paper we provide an alternative proof for the covering cover pebbling number of cycles and prove the covering cover pebbling number for a Cartesian product of paths.Item Pebbling of Oriented Graphs(2017-09) DeVries, Jerad SIn traditional graph pebbling a move across an edge is made by removing two pebbles from one vertex and adding one pebble to an adjacent vertex. We extend this concept to oriented graphs by subtracting three pebbles when moving against an edge orientation and two pebbles when moving with an edge orientation. The cover pebbling number of an oriented graph is the minimum number of pebbles such that given any initial placement of these pebbles we can simultaneously place a pebble on every vertex. In this paper we will look at pebblings of oriented paths.