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Radio Numbers of Certainm-Distant Trees
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
doi:10.1155/2014/486354
fatcat:w2bkaqxnq5br5fg7776zrrww5q