On d-distance equitable chromatic number of some graphs

Abstract

An assignment of distinct colors [Formula: see text] to the vertices [Formula: see text] and [Formula: see text] of a graph [Formula: see text] such that the distance between [Formula: see text] and [Formula: see text] is at most [Formula: see text] is called [Formula: see text]-distance coloring of [Formula: see text]. Suppose [Formula: see text] are the color classes of [Formula: see text]-distance coloring and [Formula: see text] for any [Formula: see text], then [Formula: see text] is [Formula: see text]-distance equitable colored graph. In this paper, we obtain [Formula: see text]-distance chromatic number and [Formula: see text]-distance equitable chromatic number of graphs like [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text].