@article{ajma20221012,
author={{Niazi, Zaib Hassan and Bhatti, Muhammad Awais Tariq and Aslam, Muhammad and Qayyum, Yasir and Ibrahim, Muhammad and Qayyum, Ather},
title={<i>d</i><i> </i>-Lucky Labeling of Some Special Graphs},
journal={American Journal of Mathematical Analysis},
volume={10},
number={1},
pages={3--11},
year={2022},
url={http://pubs.sciepub.com/ajma/10/1/2},
issn={2333-8431},
abstract={Consider <img src=image/abs1.png></img> as labeling of graph ¡¯s vertices. The weight for vertex <i>x </i>is specified as <img src=image/abs2.png></img> where <img src=image/abs3.png></img> shows the vertex x¡¯s degree, <img src=image/abs4.png></img> shows the <i>u</i>¡¯s open neighborhood and <i>¦Ë</i>(<i>y</i>) shows the label for vertex <i>y. </i>In [1] M. Miller et al. define <i>d</i>-lucky labeling that is similar to the graph vertex coloring. The labeling <i>¦Ë </i>is said to be <i>d?</i>lucky labeling of graph <i>G </i>if <img src=image/abs5.png></img> for each adjacent pair of vertices <i>x </i>and <i>y </i>in <i>G. </i>The least positive integer <i>n </i>such that <i>G </i>has a <i>d</i>-lucky labeling with <i>{</i>1<i>, </i>2<i>, ..., n} </i>as the set of labels is known as <i>d </i>-lucky number of a graph <i>G </i>represented as <img src=image/abs6.png></img> In this paper we investigated the <i>d</i><i>-</i>lucky number for jelly fish graph, coconut tree, kite graph, complete binary tree and generalized theta graph.},
doi={10.12691/ajma-10-1-2}
publisher={Science and Education Publishing}
}