On the Radio k-chromatic Number of Paths


A radio k-coloring of a graph G is an assignment f of positive integers (colors) to the vertices of G such that for any two vertices u and v of G, the difference between their colors is at least 1+k-d(u,v). The span rc_k(f) of f is \max\{f(v):v\in V(G)\}. The radio k-chromatic number rc_k(G) of G is min\lbrace rc_k(f) : f { is a radio k\text{-}coloring of } G\rbrace. In this paper, in an attempt to prove a conjecture on the radio k-chromatic number of path, we determine the radio k-chromatic number of paths P_n for k+5\leq n\leq\frac{7k-1}{2} if k is odd and k+4\leq n\leq\frac{5k+4}{2} if k is even.

DOI Code: 10.1285/i15900932v42n1p37

Keywords: radio k-coloring; radio k-chromatic number; radio coloring; radio number

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