Radio Numbers of Certainm-Distant Trees

Srinivasa Rao Kola, Pratima Panigrahi
2014 Journal of Discrete Mathematics  
Radio coloringof a graphGwith diameterdis an assignmentfof positive integers to the vertices ofGsuch that|f(u)-f(v)|≥1+d-d(u,v), whereuandvare any two distinct vertices ofGandd(u,v)is the distance betweenuandv. The number max{f(u):u∈V(G)}is called thespanoff. The minimum of spans over all radio colorings ofGis calledradio numberofG, denoted byrn(G). Anm-distant tree Tis a tree in which there is a pathPof maximum length such that every vertex inV(T)∖V(P)is at the most distancemfromP. This
more » ... mfromP. This pathPis called acentral path. For every treeT, there is an integermsuch thatTis 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 (orcaterpillars).
doi:10.1155/2014/486354 fatcat:w2bkaqxnq5br5fg7776zrrww5q