A radio labeling of a graph is function f:V(G)->{0,1,...,l} such that |f(u)-f(v)|>= diam(G)+1+d_G(u,v) for all u and v in V(G). The radio number of a graph G, denoted as rn(G), is the minimum span of any radio labeling of G. We provide background on some graphs with known radio numbers. We define a class of trees called biregularized paths which are formed by taking a path P and adding leaves to the vertices of P until each has the same degree m. We give bounds for the radio numbers of both the even and odd biregularized paths and give algorithms that attain each of these bounds respectively. We then discuss extending our results to a more general class of trees.

• This report represents the work of one or more WPI undergraduate students submitted to the faculty as evidence of completion of a degree requirement. WPI routinely publishes these reports on its website without editorial or peer review.

Creator

• Gottshall, Alyssa M
• Kahn, Justin David

Publisher

• Worcester Polytechnic Institute

Identifier

• E-project-031212-142536

Advisor

• Christopher, Peter R.

Year

• 2012

Date created

• 2012-03-12

Resource type

• Major Qualifying Project

Major

• Mathematical Sciences

Rights statement

• In Copyright