I have a way to represent a heptomino as an undirected graph. Each square is a vertex, when two squares' vertices touch they form an edge of length 1 in the graph.
An example heptomino and its corresponding graph:
My question is, how would I go about finding a set to describe all graphs of 7 vertices that make a heptomino? There are certain rules that must hold.
For instance, geometrically, the graph is composed of 1 and 2-simplexes. Also the degree of a vertex must be between 1 and 6.
I'm trying to find a way to know if a generated graph is a heptomino or not. This is a recreational investigation so if you notice any other interesting properties of the graph representation please let me know!