Genus-2 G-function for P1P1 orbifolds

In this paper we prove that for the Gromov–Witten theory of P1P1 orbifolds of ADE type the genus-2 G-function introduced by B. Dubrovin, S. Liu, and Y. Zhang vanishes. Together with our results in [11], this completely solves the main conjecture in their paper [4]. In the process, we also found a sufficient condition for the vanishing of the genus-2 G-function which is weaker than the condition given in our previous paper [11].