LUCKY LABELING ON SHELL FAMILY OF GRAPHS

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.