  In this paper, we study quantum modular forms in connection to quantum
invariants of plumbed 3-manifolds introduced recently by Gukov, Pei, Putrov,
and Vafa. We explicitly compute these invariants for any $3$-leg star plumbing
graphs whose associated matrix is unimodular and positive definite. For these
graphs we confirm a quantum modularity conjecture of Gukov. We also analyze the
invariants for general $n$-leg star graphs with unimodular plumbing matrices,
and prove that they can be expressed as linear combinations of quantum modular
forms.
