Mathematics – Combinatorics
Scientific paper
2010-07-15
Mathematics
Combinatorics
This paper has been withdrawn by the author due to a crucial error in Theorem 1
Scientific paper
Suppose the vertices of a graph $G$ were labeled arbitrarily by positive integers, and let $Sum(v)$ denote the sum of labels over all neighbors of vertex $v$. A labeling is lucky if the function $Sum$ is a proper coloring of $G$, that is, if we have $Sum(u) \neq Sum(v)$ whenever $u$ and $v$ are adjacent. The least integer $k$ for which a graph $G$ has a lucky labeling from the set $\lbrace 1, 2, ...,k\rbrace$ is the lucky number of $G$, denoted by $\eta(G)$. We will prove, for every graph $G$ other than $ K_{2} $, $\frac{w}{n-w+1}\leq\eta (G) \leq \Delta^{2} $ and we present an algorithm for lucky labeling of $ G $.
Ahadi Arash
Dehghan Ali
Mollaahmadi Esmael
No associations
LandOfFree
On the Lucky labeling of Graphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the Lucky labeling of Graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Lucky labeling of Graphs will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-598201