Faculty Advisor

Christopher, Peter R.

Abstract

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.

Publisher

Worcester Polytechnic Institute

Date Accepted

March 2012

Major

Mathematical Sciences

Project Type

Major Qualifying Project

Accessibility

Unrestricted

Advisor Department

Mathematical Sciences

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