LAUSR

For a simple connected graph G = (V (G),E(G)) and a positive integer k, a radio k-labelling of G is a mapping $f \colon V(G)\rightarrow \{0,1,2,\ldots \}$ such that $|f(u)-f(v)|\geqslant k+1-d(u,v)$ for each pair of distinct vertices u and v of G, where d(u,v) is the distance between u and v in G. The radio k-chromatic number is the minimum span of a radio k-labeling of G. In this article, we study the radio k-labelling problem for complete m-ary trees Tm,h and determine the exact value of radio k-chromatic number for these trees when k ≥ 2h − 1.