Niranjan, P.K.Kola, S.R.2026-02-052019AKCE International Journal of Graphs and Combinatorics, 2019, 16, 2, pp. 230-2359728600https://doi.org/10.1016/j.akcej.2017.11.007https://idr.nitk.ac.in/handle/123456789/24458For any positive integer k, a k-distance coloring of a graph G is a vertex coloring of G in which no two vertices at distance less than or equal to k receive the same color. The k-distance chromatic number of G, denoted by ?<inf>k</inf>G is the smallest integer ? for which G has a k-distance ?-coloring. In this paper, we improve the lower bound for the k-distance chromatic number of an arbitrary graph for k odd case and see that trees achieve this lower bound by determining the k-distance chromatic number of trees. Also, we find k-distance chromatic number of cycles and 2-distance chromatic number of a graph G in which every pair of cycles are edge disjoint. © 2017 Kalasalingam University2-distance chromatic numberDistance coloringk-distance chromatic number