California Lutheran University

Title: Student Research in Graph Pebbling at California Lutheran University

Director(s): Cynthia J. Wyels, Department of Mathematics and Physics

Email: wyels@clunet.edu

Dates of Program: July 11 - August 20, 2004

Summary: Graph pebbling is a technique that is used to address number-theoretical questions. Graham's conjecture states that the pebbling number of the Cartesian product of two graphs does not exceed the product of the pebbling numbers of the graph. To date Graham's conjecture has been shown to hold for several families of graphs, including trees, cliques, cycles (with small exceptions), and complete bipartite graphs [6,1,9,2]. Participants at the summer program at CLU will research Graham's conjecture for remaining cases mx C_n as well as explore the relationship between girth and pebbling number and determine optimal pebbling numbers for classes of graphs.

View Pictures From the Summer Program

Student Researchers:

• Modesty Briggs, Los Angeles, CA
• Marlene Merchain, Los Angeles, CA
• Victor M. Moreno, Fillmore, CA
• Juan Zuniga, Oxnard, CA

Program Contacts:

Bill Hawkins
MAA SUMMA
bhawkins@maa.org
202-319-8473

Michael Pearson
MAA Programs & Services
pearson@maa.org
202-319-8470

Support for NREUP is provided by the National Science Foundation's Division of Mathematical Sciences, the National Security Agency, and The Moody's Foundation.