Linear algebra certainly has applications in some of the above. But I don't think that calculus & linear algebra can be fairly described as "father & mother" to these areas. (Am I wrong? I could be missing some connections; I'm not a mathematician.)
I would say graph theory is part of combinatorics, and set theory is part of logic.
Category theory was born out of trying to abstract the relationships between different objects in abstract algebra, so is kind of the child of abstract algebra and logic. I think it's fair to say the parents of abstract algebra are combinatorics and linear algebra.
Number theory at an elementary level is combinatorics, but at higher levels branches into analytic number theory (Calculus) and algebraic number theory ((Linear) Algebra).