Let G be a connected graph and k be an integer, k ≥ 1. If l: V (G) → N is a vertex labΣeling of a graph G, then e-lucky sum of a vertex u ∈ V (G) is el(u) Σv∈N (u) l(v) + e(u), where e(u) denotes the eccentricity of u and N (u) denotes the open neighborhood of u. The labeling is e-lucky labeling if el(u) ƒ= el(v), for every uv ∈ E(G). The e-lucky number ηel(G) of G is the smallest integer k for which G has e-lucky labeling. In this paper, we compute the e-lucky number for book graph, butterfly network and complete graph. Also, we give the sharp bound for any regular bipartite self-centered graphs. © 2020. All rights reserved