Niranjan, P.K.Kola, S.R.2026-02-042022Note di Matematica, 2022, 42, 1, pp. 37-4511232536https://doi.org/10.1285/i15900932v42n1p37https://idr.nitk.ac.in/handle/123456789/22742A 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 SalentoRadio coloringRadio k-chromatic numberRadio k-coloringRadio number