My google search turned up much information about what people are doing with inductive graphs, but no definitions. So I ask you, StackExchange, what is an inductive graph? When I think of induction, I think of recursion. But this must be a wrong line of thinking, because cannot all graphs be constructed recursively? Thanks for clearing up my confusion.
A graph $G$ is $d$-inductive if the vertices of $G$ can be numbered so that each vertex has at most $d$ edges to higher-numbered vertices.
To be fair, I just used search engines as well. But let me know if either of these ring a bell:
Wikipedia thinks that inductive graphs may also be known as degenerate graphs:
On the other hand, the book The Theory of Graphs defines an inductive graph on page 13:
Do these line up with the sorts of inductive graphs you've been looking at?