J. Comp. & Math. Sci. Vol.2 (6), 874-881 (2011) Journal of Computer and Mathematical Sciences Vol. 2, Issue 6, 31 December, 2011 Pages (780-898) Radio Number of Uniform Theta Graphs BHARATI RAJAN and KINS YENOKE Department of Mathematics, Loyola College, Chennai 600 034, India ABSTRACT A radio labeling of a connected graph G is an injection f from the vertices of G to the non- negative integers ,   |  |  1  diam(G) for every two distinct vertices u and w of G. The radio number of f denoted  is the maximum number assigned to any vertex of G. The radio number of G denoted  is the minimum value of  taken over all labeling f of G. In this paper we determine bounds of the radio number of uniform theta graphs. Keywords: labeling, radio labeling, radio number and uniform theta graphs. 1. INTRODUCTION Interest in graph labeling problems began in the mid-1960’s with a conjecture of Ringel 20 and a paper by Rosa 21 . In the intervening years dozens of graph labelings techniques have been studied in over several papers. Despite the large number of papers, there are relatively few general results or methods on graph labeling. Indeed most of the results focus on particular classes of graphs and utilize ad hoc methods. Frequently, the same classes have been done by several authors. Labeled graphs serve as useful models for a broad range of applications such as coding theory, x-ray, crystallography, radar, astronomy, circuit design, channel assignments of FM radio stations and communication network addressing 2, 4 . 2. AN OVERVIEW OF THE PAPER Graph theory models for radio frequency assignment problems can be traced back to the early 1980's in the paper of Hale 11 . In 2001 Chartrand et al. 6 were motivated by regulations for channel assignments of FM radio stations to introduce radio labeling of graphs. Channels assigned to FM radio stations depend not only on the effective radiated power of their signals and the heights of their antennas but also on their distances from other stations. In wireless networks, an important task is the management of the radio spectrum that is the assignment of radio frequencies to transmitters in a way that avoid interferences. Interferences can occur if transmitters with close locations receive close frequencies.