Consider an m-valent GKM graph $(\Gamma,\alpha,\nabla)$ such that the target space of its axial function $\alpha$ is $H^{2}(BT^{n})$, where $n<m$ and $\nabla$ is a connection.

In this talk, we define the Gale dual of $(\Gamma,\alpha,\nabla)$ and give the applications to the following two geometric problems: 1. the extension problem of torus actions on GKM manifolds; 2. the computation of equivariant cohomology of some GKM manifolds.

This is joint work with Tomoo Matsumura.