eng Science and Education Publishing American Journal of Mathematical Analysis 2333-8431 2022-12-14 10 1 3 11 10.12691/ajma-10-1-2 AJMA20221012 article Zaib Hassan Niazi 1 Muhammad Awais Tariq Bhatti 2 Muhammad Aslam 2 Yasir Qayyum 2 Muhammad Ibrahim 2 Ather Qayyum atherqayyum@isp.edu.pk 2 CASPAM, Bhauddin Zakariya University Multan Pakistan Department of Mathematics, Institute of Southern Punjab Multan Pakistan Consider as labeling of graph ¡¯s vertices. The weight for vertex x is specified as where shows the vertex x¡¯s degree, shows the u¡¯s open neighborhood and ¦Ë(y) shows the label for vertex y. In [1] M. Miller et al. define d-lucky labeling that is similar to the graph vertex coloring. The labeling ¦Ë is said to be d?lucky labeling of graph G if for each adjacent pair of vertices x and y in G. The least positive integer n such that G has a d-lucky labeling with {1, 2, ..., n} as the set of labels is known as d -lucky number of a graph G represented as In this paper we investigated the d-lucky number for jelly fish graph, coconut tree, kite graph, complete binary tree and generalized theta graph. http://pubs.sciepub.com/ajma/10/1/2/ajma-10-1-2.pdf lucky labeling d -lucky labeling jelly fish graph coconut tree kite graph complete binary tree generalized theta graph