We have a graph-theory tag which covers puzzles involving graphs, for example:
but calling it 'graph-theory' is a bit prententious for a site called 'Puzzling'.
May I suggest a new tag called simply 'Graphs', or just a name change of the existing tag.
I've removed the 'graph-theory' tag from the questions in question.
On reflection, I agree the tag name is justified, but not for these questions, which could probably just use with the 'visual' tag.