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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.

solution to $K_4$
A graceful labelling of K4

All-Interval Series is a special case of a graceful graph where the graph is a line.