Generalization of the Cover Pebbling Number for Networks

Abstract

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Pebbling can be viewed as a model of resource transportation for 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 v ∈ V(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.

Keywords

• network
• tree
• path partition
• pebbling
• cover pebbling