On graceful spider graphs with at most four legs of lengths greater than one (Q670265)

Summary: A graceful labeling of a tree \(T\) with \(n\) edges is a bijection \(f:V(T) \rightarrow \{0,1, 2, \dots, n \}\) such that \(\{| f(u)-f(v)| : u v \in E(T) \}\) equal to \(\{1,2, \dots, n \}\). A spider graph is a tree with at most one vertex of degree greater than 2. We show that all spider graphs with at most four legs of lengths greater than one admit graceful labeling.