Proposed by Karen Petrie
A labelling f of the nodes of a graph with q edges is graceful if f assigns each node a unique label from 0,1,…,q and when each edge xy is labelled with |f(x)−f(y)|, the edge labels are all different. Gallian surveys graceful graphs, i.e. graphs with a graceful labelling, and lists the graphs whose status is known.
All-Interval Series is a special case of a graceful graph where the graph is a line.