Journal of Discrete Mathematics

Volume 2014, Article ID 486354, 6 pages

http://dx.doi.org/10.1155/2014/486354

## Radio Numbers of Certain -Distant Trees

^{1}Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Karnataka 575025, India^{2}Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721302, India

Received 22 August 2014; Revised 30 November 2014; Accepted 3 December 2014; Published 15 December 2014

Academic Editor: Tiziana Calamoneri

Copyright © 2014 Srinivasa Rao Kola and Pratima Panigrahi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

*Radio coloring* of a graph with diameter is an assignment of positive integers to the vertices of such that , where and are any two distinct vertices of and is the distance between and . The number max is called the *span* of . The minimum of spans over all radio colorings of is called *radio number* of , denoted by . An *m*-*distant tree T* is a tree in which there is a path of maximum length such that every vertex in is at the most distance from . This path is called a *central path*. For every tree , there is an integer such that is a -distant tree. In this paper, we determine the radio number of some -distant trees for any positive integer , and as a consequence of it, we find the radio number of a class of 1-distant trees (or *caterpillars*).