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Let $G$ be an infinite, locally finite, connected graph whose arcs (oriented edges) are labelled by letters in a finite alphabet $\Sigma$ such that arcs starting in the same vertex are labelled by ...

We can define a subclass of the regular languages. Fix an alphabet $\Sigma$. Define the "circular" languages (actually, the name already exists to denote a different thing it seems, used in the field ...

[This is a side question to Supervenience in mathematics.] There are graph properties that are not FO-definable, but MSO-, TC-, or LFP-definable. There may be other graph properties that are not MSO-,...