image-graceful labelings of partial cubes Original Research Article

Partial cubes are graphs that allow isometric embeddings into hypercubes. image-graceful labelings of partial cubes are introduced as a natural extension of graceful labelings of trees. It is shown that several classes of partial cubes are image-graceful, for instance even cycles, Fibonacci cubes, and (newly introduced) lexicographic subcubes. The Cartesian product of image-graceful partial cubes is again such and we wonder whether in fact any partial cube is image-graceful. A connection between image-graceful labelings and representations of integers in certain number systems is established. Some directions for further investigation are also proposed.