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Domination Cover Pebbling: Structural Results

Nathaniel G. Watson1, Carl R. Yerger2
1Department of Mathematics, University of California, Berkeley 850 Evans Hall, Berkeley, CA 94720-3840
2Georgia Institute of Technology, School of Mathematics, 686 Cherry Street, Atlanta, GA 30332-0160,

Abstract

This paper continues the results of “Domination Cover Pebbling: Graph Families.” An almost sharp bound for the domination cover pebbling (DCP) number, \( \psi(G) \), for graphs \( G \) with specified diameter has been computed. For graphs of diameter two, a bound for the ratio between \( \lambda(G) \), the cover pebbling number of \( G \), and \( \psi(G) \) has been computed. A variant of domination cover pebbling, called subversion DCP, is introduced, and preliminary results are discussed.