On d -distance equitable chromatic number of some graphs

An assignment of distinct colors {1, 2, 3,⋯,k} to the vertices u and v of a graph G(V,E) such that the distance between u and v is at most d is called d-distance coloring of G. Suppose C1,C2,⋯,Ck are the color classes of d-distance coloring and ||Ci|-|Cj||≤ 1 for any 1 ≤ i,j ≤ k, then G is d-distance equitable colored graph. In this paper, we obtain d-distance chromatic number and d-distance equitable chromatic number of graphs like Pm-G, Pm¯ G, Pm Pn and Pm Pn.