Dr. Charles Cusack, Hope College
Given a simple, connected graph, a pebbling configuration is a function from its vertex set to the nonnegative integers. A pebbling move between adjacent vertices removes two pebbles from one vertex and adds one pebble to the other. A vertex r is said to be reachable under a configuration if there exists a sequence of pebbling moves that places one pebble on r. A configuration is solvable if every vertex is reachable. We prove tight bounds on the number of vertices with two and three pebbles that can exist in an unsolvable configuration on a diameter two graph in terms of the size of the graph. We also prove that determining reachability of a vertex is NP-complete, even in graphs of diameter two.
Repository citation: Lewis, Timothy; Simpson, Daniel; and Taggart, Sam, "The Complexity of Pebbling in Diameter Two Graphs" (2012). 11th Annual Celebration of Undergraduate Research and Creative Performance (2012). Paper 105.
April 13, 2012.