2008/07/23 by Christian Barrientos, Barrientos, Christian
Mathematics · #05C78 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C78
paper · pdf · doi:10.48550/arxiv.0807.3738
6 pages, 6 figures
arxiv created 2008/07/23 · arxiv updated 2009/12/01
A difference vertex labeling of a graph G is an assignment f of labels to the vertices of G that induces for each edge xy the weight |f(x)-f(y)|. A difference vertex labeling f of a graph G of size n is odd-graceful if f is an injection from V(G) to 0,1,...,2n-1 such that the induced weights are 1,3,...,2n-1. We show here that any forest whose components are caterpillars is odd-graceful. We also show that every tree of diameter up to five is odd-graceful.