Graceful Labeling of some classes of Spider Graphs with Three legs greater than one

Tiang Poomsa-ard

Abstract

A spider graph is a tree with at most one vertex of degree greater

than $2$. A graceful labeling of a tree $T$ with $n$ edges is a

bijection $f:V(T) \rightarrow \{0,1,2,\ldots,n\}$ such that

$\{|f(u)-f(v)|:\{u,v\}$ is an edge of $T \} = \{1,2,\ldots,n\}$.

We show that some classes of spider graphs admit graceful labeling.