Graceful Labeling of Some Spider Graphs

Source abstract

A graceful labeling of a tree $T$ with $n$ edges is a bijection $f : V(T) \longrightarrow \{0,1,2, \ldots n\}$ such that $\{|f(u)-f(v)| : uv \in E(T)\}$ equal to $\{1,2,3,\ldots,n\}$. A spider graph is a tree with one vertex of degree at least $3$ and all others with degree at most $2$. We show that some classes of spider graphs admit graceful labeling.