Graceful graphs with pendant edges.
Christian Barrientos · Journal of International Crisis and Risk Communication Research · 2005
A graceful labeling of a graph G of size n is an injective assignment of labels from {0,1,... n} to the vertices of G such that when each edge of G has assigned a weight defined by the absolute difference of its end-vertices, the resulting weights are distinct. In this paper, we study graceful labelings of graphs with pendant edges attached; in particular, we provide graceful labelings for graphs of the form Ġ nK1and G + nK1 when G is a graceful graph with order greater than its size. We also show a graceful labeling of the unicyclic graph formed by a cycle with any number of pendant edges attached.