I am hoping to make a function that computes the graceful labeling of a graph:I have found a helpful Wolfram Resource Function https://resources.wolframcloud.com/FunctionRepository/resources/GracefulGraphFromPermutation/This will take a permutation and calculate the labeling of a graph.I am wondering if there is a way to generate a permutation that has a graceful labeling where the absolute value of the different between the vertices that are connected by the edge being labeled. For example, if nodes 3 and 7 were connected the labeling would be 4. The labeling has to be from 1 to the size of the graph. For more information, Wolfram math world is helpful https://mathworld.wolfram.com/GracefulLabeling.html and https://mathworld.wolfram.com/GracefulGraph.html
Do you have a picture of the graph you want labeled?
In general, no. It's still unsolved if all trees can be gracefully labeled.
@Rohit Namjoshi Is there a way to make a function that calculates a graceful labeling for an input graph? The resource function takes a permutation as input, so the next step would be to generate a graceful labeling permutation from an input graph.
Peter,
I don't know how to do that, but the MathWorld link has a "Download Wolfram Notebook" link on the top right. That notebook has a lot of code and examples that might help.
Take a look at this demonstrations project.
