California State University - San Bernardino

Title: Radio Labeling of Graphs

Director: Min-Lin Lo

Email: mlo@csusb.edu

Dates of Program: June 17 - July 26, 2013

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:

Reyna de Los Angeles Hernandez
Edward Jonathan Melendez
Cynthia Salgado
Jesus Mora Sanchez

Program Contacts:

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

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