Generalization of the Cover Pebbling Number for Networks - Xia, Zheng-Jiang; Hong, Zhen-Mu (Frontiers in Physics, 2020)
Pebbling can be viewed as a model of resource transportation on networks. We use a graph to denote the network. A pebbling move on a graph consists of the removal of two pebbles from a vertex and the placement of one pebble on an adjacent vertex. The t-pebbling number of a graph G is the minimum number of pebbles so that we can move t pebbles on each vertex of G regardless of the original distribution of pebbles. Let ω be a positive function on V(G), the ω-cover pebbling number of a graph G is the minimum number of pebbles so that we can reach a distribution with at least ω(v) pebbles on v for all vV(G). In this paper, we give the ω-cover pebbling number of trees for nonnegative function ω, which generalized the t-pebbling number and the traditional weighted cover pebbling number of trees.