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 λ(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 λ 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.
| [1] | Mirka Miller, Indra Rajasingh, D. Ahima Emilet, D. Azubha Jemilet, d Lucky Labeling of Graphs, 3rd International Conference on Recent Trends in Computing 2015(ICRTC-2015).View Article |
| [2] | S. Czerwinski, J. Grytczuk, V. Zelazny, Luckying labelings of graphs, Information Processing Letters, 109(18) (2009), 1078-1081.View Article |
| [3] | G. Chartrand, F. Okamoto, P. Zhang, The sigma chromatic number of a graph, Graphs and Combinatorics, 26(6) (2010), 755-773.View Article |
| [4] | M. Karonski, T. Luczak, A. Thomason, Edges weights and vertex colours, Journal of Combi- natorial Theory, Series B, 91(1) (2004), 151-157.View Article |
| [5] | Ali Asghar, Ather Qayyum and Noor Muhammad, Different Types of Topological Structures by Graphs, European Journal of Mathematical Analysis, 3 (2022).View Article |
| [6] | A. Ahadi, A. Dehghan, M. Kazemi, E. Mollaahmadi, Computation of lucky number of planar graphs is NP-hard, Inform. Process. Lett., 112(4) (2012), 109-112.View Article |
| [7] | A. Deghan, M. R. Sadeghia, A. Ahadi, The complexity of sigma chromatic number of cubic graphs, Discrete Appl. Math., submitted. |
| [8] | A. Dehghan, M.R. Sadeghi, A. Ahadi, Algorithmic complexity of proper labeling problems, Theoretical Computer Science, 495 (2013), 25-36.View Article |
| [9] | A. Dudek and D. Wajc, On the complexity of vertex-coloring edge-weightings, Discrete Math-ematics and Theoretical Computer Science, 13(3) (2011), 45-50.View Article |
| [10] | K. Manimekalai, K. Thirusangu, Pair Sum Labeling of some Special Graphs, International Journal of Computer Applications, 69(8) (2013).View Article |
| [11] | Ali Asghar, Ather Qayyum, Noor Muhamamd, Different Types of Topological Structures by Graphs, European Journal of Mathematical analysis, 3(2022).View Article |
| [12] | Generalization of Fixed-Point Approximation for Contraction and Suzuki generalized non-Expansive Mappings in Banach Domain, International journal of analysis and applications, 20 (65), (2022).View Article |
