Radio Numbers of Certain m-Distant Trees. (15th December 2014) - Kola, Srinivasa Rao; Panigrahi, Pratima
Abstract : Radio coloring of a graphG with diameterd is an assignmentf of positive integers to the vertices ofG such that| f ( u ) - f ( v ) | ≥ 1 + d - d ( u, v ), whereu andv are any two distinct vertices ofG andd ( u, v ) is the distance betweenu andv . The number max f ( u ) : u ∈ V ( G ) is called the span off . The minimum of spans over all radio colorings ofG is called radio number ofG, denoted byr n ( G ) . An m - distant tree T is a tree in which there is a pathP of maximum length such that every vertex inV ( T ) ∖ V ( P ) is at the most distancem fromP . This pathP is called a central path . For every treeT, there is an integerm such thatT is am -distant tree. In this paper, we determine the radio number of somem -distant trees for any positive integerm ≥ 2, and as a consequence of it, we find the radio number of a class of 1-distant trees (or caterpillars ).