d -Lucky Labeling of Some Special Graphs

Zaib Hassan Niazi¹, Muhammad Awais Tariq Bhatti², Muhammad Aslam², Yasir Qayyum², Muhammad Ibrahim¹ and Ather Qayyum^2,

¹CASPAM, Bhauddin Zakariya University Multan Pakistan

²Department of Mathematics, Institute of Southern Punjab Multan Pakistan

Cite this paper:
Zaib Hassan Niazi, Muhammad Awais Tariq Bhatti, Muhammad Aslam, Yasir Qayyum, Muhammad Ibrahim and Ather Qayyum. d -Lucky Labeling of Some Special Graphs. American Journal of Mathematical Analysis. 2022; 10(1):3-11. doi: 10.12691/ajma-10-1-2

Abstract

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.

Keywords:
lucky labeling d -lucky labeling jelly fish graph coconut tree kite graph complete binary tree generalized theta graph

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