Gracefulness and odd-gracefulness of compound caterpillars
Guo Jing-xia · Journal of Lanzhou University of Technology · 2012
A tree T on n vertices was called as graceful if it admits a mapping f:V(T)→{0,1,2,…,n-1} such that f(x)≠f(y) for distinct vertices x,y∈V(T) and each edge uv was labelled as f′(uv)=|f(u)-f(v)|,and the label set {f′(uv) | uv∈ E(T)}={1,2,…,n-1},where f′(uv)=|f(u)-f(v)|,and then we said f to be a graceful labeling of T.Compound caterpillars were proved to be graceful and odd-graceful by using the definition and property of the graceful tree.