On the Lucky labeling of Graphs
Arash Ahadi, Ali Dehghan, Esmael Mollaahmadi

TL;DR
This paper introduces the concept of lucky labelings in graphs, establishes bounds on the lucky number for most graphs, and provides an algorithm for constructing such labelings.
Contribution
It defines lucky labelings, proves bounds on the lucky number for all graphs except K2, and presents an algorithm for lucky labeling.
Findings
Lucky number bounds between rac{w}{n-w+1} and riangle^2.
The bounds apply to all graphs except K2.
An algorithm for constructing lucky labelings is provided.
Abstract
Suppose the vertices of a graph were labeled arbitrarily by positive integers, and let denote the sum of labels over all neighbors of vertex . A labeling is lucky if the function is a proper coloring of , that is, if we have whenever and are adjacent. The least integer for which a graph has a lucky labeling from the set is the lucky number of , denoted by . We will prove, for every graph other than , and we present an algorithm for lucky labeling of .
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Taxonomy
TopicsGraph Labeling and Dimension Problems · graph theory and CDMA systems
