# Radio Labeling for Cycle Graphs

## Authors:

*Lydia Delgado, Ilia Gonzales, Joel Webster*

## Mentor:

*Min-Lin Lo, Associate Professor of Mathematics , California State University San Bernardino*

Let G be a connected graph. For any two vertices u and v, let d(u, v) denote the distance between u and v in G. The maximum distance between any pair of vertices is called the diameter of G and denoted by diam(G). A radio labeling (or multi-level distance labeling) of a connected graph G is a function f : V(G) → {0, 1, 2, 3,…} with the property that |f(u) – f(v)| ≥ diam(G) – d(u, v) + 1 for every two distinct vertices u and v of G. The span of f is defined as max u,v∈ V(G) {|f(u) – f(v)|}. The radio number of G is the minimum span over all radiolabeling of G. In this presentation we will discuss the progress we made towards finding the radio number for cycle graphs during a 2012 summer research program, which is a part of the NSF PRISM grant DMS-1035120 (Proactive Recruitment in Introductory Science and Mathematics).

## Presented by:

*Ilia Gonzales, Joel Webster, Lydia Delgado*

## Date:

*Saturday, November 17, 2012*

## Time:

*4:15 PM — 4:30 PM*

## Room:

*Bell Tower 1491*

## Presentation Type:

*Oral Presentation*

## Discipline:

*Mathematics*