Abstract

Let $f : V(G) \rightarrow N$ be a labeling of the vertices of a graph $G$. Let $S(v)$ denote the sum of labels of the neighbours of the vertex $v$ in $G$. If $v$ is an isolated vertex of $G$, then $S(v) = 0$. A labeling $f$ is lucky if $S(u) \neq S(v)$ for every pair of adjacent vertices $u$ and $v$. The lucky number of a graph $G$, denoted by $\eta(G)$, is the least positive integer $k$ such that $G$ has a lucky labeling with $\{1, 2,..., k\}$ as the set of labels. In this paper we prove that shell graph, bow graph and wheel graph admits Lucky labeling.

Keywords and Phrases

Lucky Labeling, Shell Graph, Bow Graph, Wheel Graph, Lucky number.

A.M.S. subject classification

05C78.

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