Let l : V (G) → N be a labeling of the vertices of a graph G by positive integers. Define c(u) =v∈N(u) l(v) + d(u), where d(u) denotes the degree of u and N(u) denotes the open neighborhood of u. We define a labeling l as d-lucky if c(u) = c(v), for every pair of adjacent vertices u and v in G. The d-lucky number of a graph G, denoted by ηdl(G), is the least positive k such that G has a d-lucky labeling with {1, 2, . . ., k} as the set of labels. The problem is also studied as a graph coloring problem. In this paper we find the dlucky number of certain cyclic graphs like cycle of ladder, n-sunlet graphs and helm graphs. © 2016 Academic Press. All Rights Reserved.