On the Radio k-chromatic Number of Paths

Abstract

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 rck(f) of f is (Formula Presented). The radio k-chromatic number (Formula Presented). 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<inf>n</inf> for (Formula Presented) if k is odd and (Formula Presented) if k is even. © 2022 Università del Salento