California State University - San Bernardino

Title: Radio Number for Square Cycles and Cube Cycles

Director:

Min-Lin Lo

Email:

mlo@csusb.edu

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 ƒ (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)+|ƒ(u)-ƒ(v)|≥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