It is well known that the first order theory of graphs (i.e., an irreflexive and symmetric "edge" relation on a set) is undecidable. The same holds for the first order theory of finite graphs.

*I am interested to know about subclasses of finite graphs such that its first-order theory is also known to be undecidable*. Any suggestion about where to look for this kind of results? I am particularly interested on any resource (url, survey paper, etc.) gathering results of this kind.

One example of the kind of results I search for is that the first order theory of all finite bipartite graphs with at least three elements is known to be undecidable. Any other subclasses which are also known undecidable?