Year: 2009
Type: preprint
Abstract: We prove a generalization of Graham's Conjecture for optimal pebbling with arbitrary sets of target distributions. We provide bounds on optimal pebbling numbers of products of complete graphs and explicitly find optimal $t$-pebbling numbers for specific such products. We obtain bounds on optimal pebbling numbers of powers of the cycle $C_5$. Finally, we present explicit distributions which provide asymptotic bounds on optimal pebbling numbers of hypercubes.
Source: arXiv (Cornell University)
Institutions: Quinnipiac University, Arizona State University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2132233728