053: Graceful Graphs

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 ${0, 1, \ldots , q}$ 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.