Mathematical notation for formulas involving trees

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I am working on document that requires me to write such things as "$T_1$ is a descendant of $T_0$", or "$N_1$ is an parent of $N_2$". For now, I've been highjacking set notation for use in formulas, like

$$ f(A) = \sum_{B\subset A}g(B) $$

where $B$ are descendants of $A$, but as I run into more relationships (e.g. parent vs ancestor) I find myself having to invent some notation.

Is there an existing (and hopefully well-established) notation associated with tree relationships which I can use in formulas instead of having to invent my own?