California State University - San Bernardino
Title:
Radio Number for Square Cycles and Cube Cycles
Director:
Email:
Dates of Program: June 21 - July 30, 2010
Summary:
In 2001, Chartrand, Erwin, Zhang, and Harary were motivated by regulations for channel
assignments of FM radio stations to introduce radio labeling of graphs. A radio labeling
of a connected graph G is a function Æ? (think of it as a channel assignment) from the vertices, V(G),
of G to the natural numbers such that for any two distinct vertices u and v of G:
- (Distance of u and v)+|Æ?(u)-Æ?(v)|â?¥1+(maximum distance over all pairs of vertices of G).
The radio number for G, rn(G), is the minimum span of a radio labeling for G. Finding the
radio number for a graph is an interesting, yet challenging, task. So far, the value is known
only for very limited families of graphs. The objective of this project is to investigate
the radio number of different types of graphs. We will attempt to extend the study to categories
of graphs whose radio numbers are not yet known.
Student Researchers Supported by MAA:
- Lynette Mejia
- Nolberto Rezola
- Georgina Santos
- Nicole Smith
Program Contacts:
Bill Hawkins
MAA SUMMA
bhawkins@maa.org
202-319-8473
Michael Pearson
MAA Programs & Services
pearson@maa.org
202-319-8470