The \(t\)-pebbling number of the complete graph with a missing edge (Q2799867)

Given a distribution of pebbles \(p:V\to \mathbb N\cup \{0\}\) on the vertices of a connected graph \(G=(V,E)\), a pebbling move removes two pebbles at a vertex \(v\) and places one pebble at an adjacent vertex \(u\). One pebble is the cost of transportation along the edge \(vu\). A vertex is \(t\)-reachable if \(t\) pebbles can be moved to the vertex using pebbling moves. The \(t\)-pebbling number of a graph \(\pi_t(G)\) is the minimum number of pebbles that ensures that any vertex is \(t\)-reachable from any initial distribution of the pebbles.NEWLINENEWLINEThe main result of the paper is the \(t\)-pebbling number of the complete graph with a missing edge: \(\pi_t(K_n-e)=\max\{4t,n-2+2t\}\).